JP3855038B2 - Rigid body motion measuring method, rigid body motion measuring device, rigid body motion measuring program, jaw motion measuring method, jaw motion measuring device and jaw motion measuring program - Google Patents

Description

ここでＴ_LCは下顎と特定の位置関係を持つ座標系からビデオカメラ１７の座標系への変換を表し、Ｃ_X、Ｃ_Y、Ｃ_Zはビデオカメラ１７の座標系から見た位置座標、Ｌ_X、Ｌ_Y、Ｌ_Zは下顎と特定の位置関係を持つ座標系から見た位置座標、Ｇ_CLは単位ベクトルの回転変換を表す三行三列の行列、ａ_CLは三行一列のベクトルである。今の場合Ｌ_X、Ｌ_Y、Ｌ_Zは原点であるからいずれもゼロである。この式（１）の演算により、特定点Ｌ_Oの三次元座標および三次元回転角が算出される。
【００３２】
同様に、上顎と特定の位置関係を持つ座標系の特定点Ｕ_O、特定点Ｕ_Oを原点とする単位ベクトルＵ_OＵ_X、Ｕ_OＵ_Y、Ｕ_OＵ_Zを定められる。つぎにこの特定点Ｕ_Oの位置座標を、ビデオカメラ１７の座標系から測定したときの位置座標への変換Ｔ_UCは、式（２）で算出される。
【数２】

記号の意味は、式１と同様である。
【００３３】
すなわちこの処理手順は、コンピュータ１９において、下顎、上顎のマーカー座標測定値をメモリー部３５から読み出して、演算部３７で、下顎、上顎とそれぞれ特定の位置関係を持つ特定点と単位ベクトルを定め、式（１）、（２）を演算し、算出したデータは、メモリー部３５に格納する。
【００３４】
ＳＴＥＰ３は、上顎特定点の座標、単位ベクトルを基準として変換する処理手順である。ＳＴＥＰ２の式（１）、式（２）の演算で得られた、特定点Ｌ_Oおよび特定点Ｕ_Oのビデオカメラ１７の座標系から測定したときの位置座標から、上顎と特定の位置関係を持つ特定点Ｕ_Oの三次元座標、単位ベクトルを基準にして、下顎と特定の位置関係を持つ特定点Ｌ_Oの三次元座標、三次元回転角を変換する。
【００３５】
一般に、ＡからＢへの変換をＴ_AB、ＢからＣへの変換をＴ_BC、ＣからＡへの変換をＴ_CAとすると、これら三者間に式（３）が成り立つ。
【数３】
Ｔ_CAｏＴ_BCｏＴ_AB＝１
Ｔ_BC＝Ｔ_CA ^-1ｏＴ_AB ^-1＝Ｔ_CA ^-1ｏＴ_BA ・・・（３）
ここで、例えばＴ_BCｏＴ_ABは、Ｔ_ABに変換Ｔ_BCを施したことを表すものとする。したがって、いまＡをビデオカメラの座標系、Ｂを下顎と特定の位置関係を持つ座標系、Ｃを上顎と特定の位置関係を持つ座標系とすると、下顎と特定の位置関係を持つ特定点Ｌ_Oの三次元座標、三次元回転角を、上顎と特定の位置関係を持つ特定点Ｕ_Oの三次元座標、単位ベクトルを基準にして変換するときの変換Ｔ_LUは、式（１）のＴ_LC、式（２）のＴ_UCから式（４）で算出される。
【数４】
Ｔ_LU＝Ｔ_UC ^-1ｏＴ_LC ・・・（４）
このようにして得られたＴ_LUを用いて、上顎と下顎が相互に相対運動をしたときでも、上顎を基準に下顎の運動を捉えることができるので、以後は特に断らない限り、この上顎基準の下顎の運動を考える。
【００３６】
すなわちこの処理手順は、コンピュータ１９において、メモリー部３５に格納されている、下顎と特定の位置関係をもつ特定点の三次元座標および三次元回転角と、上顎と特定の位置関係をもつ特定点の三次元座標および三次元回転角のデータを読み出し、これを演算部３７において、上顎に固定した座標系を基準として、下顎の特定点の三次元座標および三次元回転角のデータを座標変換する。座標変換したデータは、メモリー部３５に格納する。
【００３７】
ＳＴＥＰ４は、相対運動中であるかどうか判断し、相対運動中のときは、ＳＴＥＰ１からＳＴＥＰ３までを繰り返し、相対運動が終了し、データ測定の必要がなくなれば、ＳＴＥＰ１からＳＴＥＰ３までの処理を終了し、次のＳＴＥＰ５に進む。例えば一連の相対運動を３００フレームの動画データで測定するときは、約１０秒でＳＴＥＰ１からＳＴＥＰ３までの処理を終了する。
【００３８】
ＳＴＥＰ５は、運動位置の変化を示す行列算出の処理手順である。一般に空間における運動は回転と平行移動の合成である。空間にある座標系を定めると、空間の点は三次元のベクトルとして表現できるので、今ある空間点をＭとして、ｘをそのベクトルとする。運動により点Ｍを動かすとき、その運動後の座標は、回転を表す行列Ｇとベクトルａを用いて、Ｇｘ＋ａと表される。これを行列の積で示すために、三行一列のｘにもう一行１を加えた四行一列として、式（５）のように表す。
【数５】

つまり、点Ｍの運動は、回転をあらわす三行三列の行列成分Ｇと、三行一列の行列成分であるベクトルａを含む四行四列の行列で表すことができる。
【００３９】
いま下顎の特定点Ｌ_Oについて第一の運動位置を表す四行四列の行列をＨ_1Uと、第二の運動位置を表す四行四列の行列をＨ_2Uとすると、これらはそれぞれ第一の運動位置、第二の運動位置から上顎の特定点Ｕ_Oへの変換に相当する。式（３）の関係を用いれば、下顎の特定点Ｌ_Oについて第一の運動位置から第二の運動位置への運動をあらわす変換Ｈ₁₂は、式（６）で表される。
【数６】
Ｈ₁₂＝Ｈ_2U ^-1ｏＨ_1U ・・・（６）
【００４０】
すなわちこの処理手順は、コンピュータ１９において、メモリー部３５に格納された式（４）のＴ_LUのデータから、第一の運動状態、第二の運動状態におけるデータを読み出し、それぞれＨ_1U、Ｈ_2Uとして、演算部３７において式（６）を演算することで、第一の剛体に固定した座標系を基準にした、前記特定点の第一の運動位置から第二の運動位置への運動位置の変化をあらわす運動行列を演算し、その結果をメモリー部３５に格納する。
【００４１】
ＳＴＥＰ６は、回転座標系の単位ベクトル算出の処理手順である。回転中心を通る回転軸方向の単位ベクトルは、回転を表す行列Ｇの、固有値１を持つ固有ベクトルであるから、式（６）で演算された四行四列の行列Ｈ₁₂の回転を表す三行三列の行列成分Ｇについて、その固有値が１である固有ベクトルを、よく知られた掃き出し法などを用いて算出して回転軸方向の単位ベクトルを定め、残りの二軸の単位ベクトルもその過程で演算する。
【００４２】
すなわちこの処理手順は、コンピュータ１９においてメモリー部３５に格納された四行四列の行列Ｈ₁₂を読み出して、演算部３７において、その回転を表す三行三列の行列の行列について、固有値１の固有ベクトルを求める演算処理を行い、その結果をメモリー部３５に格納する。
【００４３】
ＳＴＥＰ７は、回転角算出の処理手順である。ＳＴＥＰ６で得られた回転座標系の単位ベクトルをＰとすると、式（７）の関係にあることはよく知られている。
【数７】

ここでθが、剛体の回転軸周りの回転角を表す。すなわちコンピュータ１９において、メモリー部３５に格納されているＨ₁₂のデータと、固有ベクトルＰを読み出して、式（７）を演算し、その結果をメモリー部３５に格納する。
【００４４】
ＳＴＥＰ８は、回転中心座標算出の処理手順である。下顎と特定の位置関係をもつ特定点Ｌ_Oの第一の運動位置から第二の運動位置への運動をあらわす運動行列Ｈ₁₂のベクトル成分ａについて、式（８）で示すように、ａを回転座標系でみれば、回転軸方向の回転中心の平行移動成分ｂ₁と、回転中心周りの回転角θによる座標移動成分ｂ₀に分けられる。
【数８】

ここでａは三行一列、ｂ₀は二行一列、ｂ₁はスカラー量である。ｂ₀は、回転中心から特定点Ｌ_Oへの回転半径をｃ₀とすれば、式（９）の関係を持つ。
【数９】
ｂ₀＝ｃ₀−Ｇ＊ｃ₀
ｃ₀＝（Ｉ−Ｇ）^-1＊ｂ₀ ・・・（９）
ここでＩは単位行列である。このｃ₀と特定点Ｌ_Oの位置座標から回転中心の位置座標が算出できる。すなわち、コンピュータ１９において、メモリー部３５に格納されているＨ₁₂を読み出し、演算部３７でベクトル成分ａについて式（８）、（９）を演算し、回転中心座標を算出し、結果をメモリー部３５に格納する。
【００４５】
ＳＴＥＰ９は、メモリー部３５に格納されている一連の相対運動のデータについて、ＳＴＥＰ５からＳＴＥＰ８の処理手順がすべて完了したか判断し、未完了のときはＳＴＥＰ１からＳＴＥＰ３までの処理を終了の処理手順を繰り返し、完了したときはつぎのＳＴＥＰ１０に進む。例えば一連の相対運動を３００フレームの動画データから演算するときは、約五分でＳＴＥＰ１からＳＴＥＰ３までの処理を終了する。
【００４６】
ＳＴＥＰ１０は、表示の処理手順である。回転軸を含む回転座標系の単位ベクトル、回転軸回りの回転角、回転中心座標の少なくとも一つの回転運動特性値を表示する。すなわちコンピュータ１９において、メモリー部３５から、これらの回転運動特性値を読み出して、出力部３９を介してコンピュータのＣＲＴ画面、プロッタ等の表示装置３８に表示する。
【００４７】
図８は、本発明の実施の形態における測定結果の例であり、図８（ａ）は健常者について、図８（ｂ）はクリック症状を有する患者について、上顎に対して下顎を次第に開き次いで次第に閉じる運動を行ない、横軸に時間（画像フレーム番号）をとり、縦軸にその時々刻々の下顎の回転軸に対しての回転角、回転中心位置座標、回転単位ベクトル、回転中心の平行移動量を表したものである。図８（ａ）と図８（ｂ）を比較すると図中で（１）、（２）、（３）と示した点が異なる。これらの運動位置においては、回転中心が移動し、その単位ベクトルも変化ているのが明確に認められる。すなわち、（１）と（３）の点においては、下顎と上顎とのかみ合わせの開始および終了したときに、かみ合わせにおいて正常に上顎と下顎が接触しないかみ合い相異常があることがわかり、（２）の点においては顎の開閉運動に不連続性があり、ときには「クリック」音が認められる運動相異常があることが分かる。このように上顎、下顎のかみ合わせ、開閉という二個の剛体の機能で特徴づけられる相対的な運動を回転角、回転中心座標、単位ベクトル、回転中心の平行移動等、回転運動特性値として定量的に測定し、その結果を表示できる。
【００４８】
本発明の実施の形態においては、下顎運動に詳細に説明したが、ひざ、腕、指等関節の回転運動機能で特徴づけられる二個の剛体の相対的な運動について本発明が実施できる。この場合、被検体は人間、人間以外の生体に限られず、ロボットについても本発明は実施できる。また機械装置の一部の機構等、相互に相対運動をする第一の剛体と第二の剛体間の剛体運動の測定にも本発明は実施できる。
【００４９】
表示については、さらに座標変換をほどこして、観察しやすい座標系で測定値を表示することでも本発明は実施できる。
【００５０】
本発明の実施の形態におけるフローチャートのうち、ＳＴＥＰ１からＳＴＥＰ１０までをひとつのプログラムとすることも、ＳＴＥＰ１からＳＴＥＰ３までと、ＳＴＥＰ４以降を分離して二つのプログラムとすることによっても本発明を実施することができる。
【００５１】
マーカーの大きさ、形状、色彩等は、本発明の実施の形態のほか、反射型のマーカーを各実施の態様に合わせて設計事項の範囲で変更して本発明が実施できる。位置座標測定原理は、本発明の実施の形態のほか、複数台の非接触式、接触式の三次元測定器によっても本発明が実施できる。
【００５２】
【発明の効果】
本発明にかかる剛体運動測定方法は、相互に相対運動をする第一の剛体および第二の剛体にそれぞれ複数のマーカーを取付け固定し、相対運動中の前記複数のマーカーの三次元座標を測定し、第二の剛体と特定の位置関係をもつ特定点の三次元座標および三次元回転角を、第一の剛体に固定した座標系を基準にして演算し、相対運動中の第一の運動位置と第二の運動位置で得られた、前記特定点の二個の三次元六自由度演算結果から、第一の剛体に固定した座標系を基準にした、前記特定点の第一の運動位置から第二の運動位置への運動位置の変化をあらわす行列を演算する運動行列演算工程と、前記演算で得られた運動行列を、剛体の回転座標系基準の回転運動行列に変換し、第二の剛体の回転運動特性値として、回転軸を含む回転座標系の単位ベクトル、回転軸回りの回転角、回転中心座標を演算するので、これらの回転運動特性値を追跡することで、二個の剛体の機能で特徴づけられる相対的な回転運動の変化を定量的に測定ができた。
【００５３】
さらに本発明の顎運動測定方法においては、被検体の上顎および被検体の下顎に取付けられる複数のマーカーは、反射型のマーカーであるので、一般室での測定が可能となった。
【図面の簡単な説明】
【図１】 本発明の実施の形態にかかる顎運動測定装置の使用状況説明図
である。
【図２】 本発明の実施の形態におけるヘッドフレーム、下顎マーカー具の詳細図である。
【図３】 本発明の実施の形態における光学系の配置図である。
【図４】 本発明の実施の形態におけるコンピュータのブロック図である。
【図５】 本発明の実施の形態におけるマーカーの位置座標測定原理を示す図である。
【図６】 本発明の実施の形態におけるフローチャートである。
【図７】 本発明の実施の形態における特定点、単位ベクトルの定義の説明図である。
【図８】 本発明の実施の形態における測定結果の例で、（ａ）は健常者、（ｂ）は「クリック」症状者についてのものである。
【図９】 従来例の下顎運動測定装置の原理図である。
【図１０】 従来例の顎の開閉による座標の変化の測定結果の例である。
【符号の説明】
１ 被検体、２ 下顎、３ 上顎、４ フェースボー（Ｌ）、５ フェースボー（Ｕ）、６ ＬＥＤ、７ 座標系Σ_L、８ 座標系Σ_U、９ カメラ座標系Σ、１０ 座標系Σ_H、１１ マーカー、１２ ヘッドフレーム、１３ 下顎マーカー具、１４ 測定台、１５、１５ａ、１５ｂ 第一反射鏡、１６、１６ａ、１６ｂ 第二反射鏡、１７ ビデオカメラ（三次元測定器）、１８ 信号ケーブル、１９ コンピュータ、２０，２１ フレーム体、２２ 帯材、２３ 締め付け部分、２４ 取付板、２５ マウスピース、２６ 光路、３１ キーボード、３２入力部、３３ 三次元測定器インタフェイス、３４ 制御部、３５ メモリー部、３６ 外部記憶装置、３７ 演算部、３８ 表示装置、３９ 出力部。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a rigid body motion measuring method, a rigid body motion measuring apparatus, and a rigid body motion measuring program between a first rigid body and a second rigid body that move relative to each other, and in particular, a relative characteristic characterized by the functions of two rigid bodies. Further, the present invention relates to a jaw motion measurement method, a jaw motion measurement device, and a jaw motion measurement program for measuring the relative motion state of the upper jaw and the lower jaw of a subject.
[0002]
[Prior art]
Conventionally, in order to measure the motion of a rigid body, a method has been adopted in which a marker is attached and fixed to the rigid body, the position coordinates of the marker are measured with a three-dimensional coordinate measuring instrument, and the change of the position coordinates is displayed on a plotter or the like. ing. However, in order to measure the motion of two rigid bodies that make relative motions, it is necessary to determine the relative three-dimensional coordinate position, and in particular, the relative motion of two rigid bodies characterized by functions such as rotational motion of joints. As for, it is necessary to devise measurement focusing on its function. An example of this is the measurement of jaw movement. Opening and closing of the jaw is performed by relative movement of the upper jaw and the lower jaw. However, the opening and closing of the jaw may occur during the growth of the individual or due to a disease or an accident. For example, there is a meshing phase abnormality in which the upper and lower jaws do not normally come into contact with each other, there is a discontinuity in the opening and closing movement of the jaw, and a movement phase abnormality in which a `` click '' sound is sometimes observed. A quantitative measurement of movement is required.
[0003]
FIG. 9 shows a principle diagram of a conventional mandibular movement measuring apparatus disclosed in Japanese Patent Laid-Open No. 7-308329. In FIG. 9, a face bow (L) 4 and a face bow (U) 5 are attached and fixed to the lower jaw 2 and upper jaw 3 of a subject 1 with an adhesive or a suitable band, and each face bow is attached to the left and right sides of the jaw, respectively. A total of eight LEDs 6 are provided, two for each of the LEDs 6. Although not shown in the figure, three cameras that are responsible for coordinate measurement on the x-axis, y-axis, and z-axis are respectively installed on the left and right sides of the jaw where the position coordinates of the LED 6 can be measured. The camera is connected to a coordinate system calculation means (not shown), and the LED 6, the camera, and the coordinate system calculation means are connected to a CPU (not shown).
[0004]
The operation of the conventional example with this configuration will be described. 8 LEDs 6 are sequentially turned on in accordance with instructions from the CPU not shown in FIG. 8, and the coordinates of the LEDs 6 turned on by three cameras installed on the right or left of the chin are measured each time the lights are turned on. The camera coordinate system 9 indicated by Σ and Σ<sub>L</sub>Conversion T between the coordinate system (mandible coordinate system) 7 fixed to the lower jaw indicated by<sub>1</sub>, Σ, camera coordinate system 9 and Σ<sub>U</sub>The transformation T between the coordinate system (maxillary coordinate system) 8 fixed to the maxilla indicated by<sub>2</sub>Using the mandibular coordinate system (Σ<sub>L</sub>) 7 to maxillary coordinate system (Σ<sub>U</sub>) 8 conversions are computed. By this transformation, maxillary coordinate system (Σ<sub>U</sub>) The position coordinates of the specific point (measurement point) of the lower jaw obtained from 8 can be obtained, and even if the upper jaw and the lower jaw move relative to each other, the change in the position coordinates of the specific point of the lower jaw relative to the upper jaw can be tracked.
[0005]
Furthermore, it is a plane that is perpendicular to the horizontal plane including the indentation point and the left and right ears, and the horizontal plane, and is a plane in the center in front of the head. Σ composed of three frontal planes<sub>H</sub>Is set, and the upper coordinate system (Σ<sub>U</sub>) 8 and coordinate system (Σ<sub>H</sub>) Conversion T between 10<sub>Three</sub>Using the mandibular coordinate system (Σ<sub>L</sub>) 7 and coordinate system (Σ<sub>H</sub>) Conversion T between 10<sub>Four</sub>And the coordinate change of the specific point of the lower jaw 2 is converted to the horizontal plane, the sagittal plane, and the frontal plane. By this conversion, the change in coordinates on the horizontal plane, the sagittal plane, and the frontal plane of the specific point of the lower jaw 2 due to the opening and closing of the jaw can be traced, and FIG. 10 shows an example of the calculation result displayed on the plotter.
[0006]
[Problems to be solved by the invention]
As described above, even when the first rigid body and the second rigid body move relative to each other, for example, even when the upper jaw and the lower jaw move relative to each other in the conventional example, the upper jaw can be obtained by using the coordinate transformation calculation. It is possible to obtain a change in position coordinates of a specific point of the lower jaw with respect to, and a change in position coordinates of a specific point of the lower jaw on the horizontal plane, the sagittal plane, and the frontal plane. However, what is obtained is a change in the relative position coordinates of a specific point on the lower jaw, the meshing phase abnormality where the upper and lower jaws do not normally contact in meshing, discontinuity in the jaw opening and closing movement, sometimes `` click '' For movement phase abnormalities, etc. in which sound is recognized, it is difficult to estimate the rotational movement abnormalities that are characterized by the function of the jaws, because the position coordinates change very slightly.
[0007]
In addition, when the subject is related to human motor function, such as jaw movement, there is a problem of measurement environment. For example, in the conventional measurement method described above, in order to increase the measurement accuracy of the position coordinates, it is necessary to perform the measurement by sequentially turning on the LEDs in an isolated dark room so as not to make a shadow of the LED. It is close to the situation of flashing sequentially, and it gives mental pressure to the patient, especially pediatric patients.
[0008]
The object of the present invention is to solve the problems of the conventional example, and to perform a rigid body motion between the first rigid body and the second rigid body that move relative to each other, in particular, the relative motion characterized by the functions of the two rigid bodies. In addition, in the measurement of jaw movement that measures the relative movement state of the subject's upper and lower jaws, there is a discontinuity in the meshing phase abnormality where the upper and lower jaws do not normally contact in engagement, the jaw opening and closing movements are Rigid body motion measurement method, rigid body that can quantitatively measure the relative rotational motion characterized by jaw function, such as abnormal movement phase where sometimes “click” sound is recognized, and can be measured in a general room To provide a motion measurement device, a rigid motion measurement program, a jaw motion measurement method, a jaw motion measurement device, and a jaw motion measurement program.
[0009]
[Means for Solving the Problems]
  In order to achieve the above object, the rigid body motion measuring method according to the present invention is applied to the first rigid body and the second rigid body, which perform relative motion to each other.Mounting fixed3D coordinates of the markers in relative motionWith a three-dimensional measuring instrumentFrom the three-dimensional measurement step to be measured and the three-dimensional coordinate measurement value obtained during the relative motion, the three-dimensional coordinates and the three-dimensional rotation angle of the specific point having a specific positional relationship with the second rigid body are determined as the first Based on a coordinate system fixed to a rigid bodyBy computing meansIn a rigid body motion measurement method having a three-dimensional six-degree-of-freedom calculation step for calculating, two three-dimensional six-degree-of-freedom calculations of the specific point obtained at the first motion position and the second motion position during relative motion From the result, a matrix representing a change in the movement position from the first movement position of the specific point to the second movement position based on the coordinate system fixed to the first rigid body is obtained.By computing meansThe motion matrix calculation step to calculate, and the motion matrix obtained by the above calculation is converted into a rotational motion matrix based on the rotational coordinate system of the rigid body, and the unit vector or rotation of the rotational coordinate system including the rotational axis of the second rigid body At least one rotational motion characteristic value of the rotation angle around the axis or the rotation center coordinateBy computing meansIt has the rotational motion calculating process to calculate, It is characterized by the above-mentioned.
[0010]
  In the rigid body motion measuring method according to the present invention, the motion matrix calculation step includes a matrix component representing a rotation of 3 rows and 3 columns and a matrix having a vector component of 3 rows and 1 column.By computing meansIt is characterized by calculating.
[0011]
  Further, the rigid body motion measuring apparatus according to the present invention includes a plurality of markers that are respectively attached and fixed to the first rigid body and the second rigid body that move relative to each other, and three-dimensional coordinates of the plurality of markers that are in relative motion. From the three-dimensional measuring device to be measured and the three-dimensional coordinate measurement value obtained during the relative motion, the three-dimensional coordinates and the three-dimensional rotation angle of the specific point having a specific positional relationship with the second rigid body are determined as the first In the rigid body motion measuring apparatus having a three-dimensional 6-degree-of-freedom calculating means for calculating based on a coordinate system fixed to a rigid body, the specific point obtained at the first motion position and the second motion position during relative motion From the two three-dimensional six-degree-of-freedom calculation results of, the change of the movement position from the first movement position to the second movement position of the specific point is shown based on the coordinate system fixed to the first rigid body. A motion matrix computing means for computing a matrix; The movement matrix obtained by calculation, converts the rotary motion matrix of the rotating coordinate system based rigid, the second rigidAt least one of the unit vector of the rotation coordinate system including the rotation axis, the rotation angle around the rotation axis, or the rotation center coordinateAnd a rotary motion calculating means for calculating a rotational motion characteristic value of the rigid body.
[0012]
  Further, in the rigid body motion measuring apparatus according to the present invention, the motion matrix computing means represents a matrix having a matrix component representing a rotation in three rows and three columns and a vector component having three rows and one column.CalculateIt has at least one calculating means of the rotation center calculating means.
[0013]
  Further, the rigid body motion measurement program according to the present invention includes a computer that measures the motion of a rigid body, and a plurality of markers that are respectively attached and fixed to the first rigid body and the second rigid body that are relatively moved by the control unit. Instructs a three-dimensional measuring instrument that measures three-dimensional coordinates, takes the measured three-dimensional coordinate values during relative movement into the memory part of the computer, stores them in the memory part, and stores them in the memory part by the computing part of the computer The measured three-dimensional coordinate value is read, and the three-dimensional coordinates and the three-dimensional rotation angle of a specific point having a specific positional relationship with the second rigid body are calculated with reference to the coordinate system fixed to the first rigid body. In the rigid body motion measurement program for executing the three-dimensional six-degree-of-freedom computation processing procedure, the computer motion unit further determines the first motion position during relative motion and From the two three-dimensional 6-degree-of-freedom calculation results of the specific point obtained at the second motion position, the first motion position of the specific point is determined based on the coordinate system fixed to the first rigid body. A motion matrix calculation processing procedure for calculating a matrix representing a change of the motion position to the second motion position, and converting the motion matrix obtained by the calculation into a rotational motion matrix based on a rotational coordinate system of a rigid body; Rigid bodyAt least one of the unit vector of the rotation coordinate system including the rotation axis, the rotation angle around the rotation axis, or the rotation center coordinateThe rotational motion calculation processing procedure for calculating the rotational motion characteristic value of the is executed.
[0015]
  In the rigid body motion measurement program according to the present invention, the motion matrix computation processing procedure computes a matrix having a matrix component representing rotation in three rows and three columns and a matrix having vector components in three rows and one column.Make senseIt is characterized by that.
[0016]
  In the jaw movement measuring method according to the present invention, the first rigid bodyTheMaxilla of subjectageThe second rigid bodyTheLower jaw of subjectAs a result, the three-dimensional coordinates of the plurality of markers in the relative movement, which are attached and fixed to the upper jaw of the subject and the lower jaw of the subject, which move relative to each other, are measured by a three-dimensional measuring instrument.It is characterized by that. The same applies to the jaw movement measuring device and the jaw movement measuring program.
[0017]
  How to measure jaw movement of the present inventionTo the lawThe plurality of markers attached to the upper jaw of the subject and the lower jaw of the subject are preferably reflective markers.The same applies to the jaw movement measuring device and the jaw movement measuring program.
[0018]
  In the rigid body motion measuring method according to the present invention, a plurality of markers are attached and fixed to each of the first rigid body and the second rigid body that move relative to each other, and the three-dimensional coordinates of the plurality of markers during the relative motion are measured. Calculate the 3D coordinates and 3D rotation angle of a specific point with a specific positional relationship with the second rigid body based on the coordinate system fixed to the first rigid body, and the first motion position in relative motion The first movement position of the specific point based on the coordinate system fixed to the first rigid body from the two three-dimensional six-degree-of-freedom calculation results of the specific point obtained at the second movement position. A motion matrix calculation step for calculating a matrix representing a change in the movement position from the first movement position to the second movement position, and converting the movement matrix obtained by the calculation into a rotation movement matrix based on a rotational coordinate system of a rigid body; Because it calculates the rotational motion characteristic value of the rigid body of In relative rotational movement characterized, it is quantitatively measured using a rotational movement characteristic values of the rigid body.Here, the rotational motion characteristic value is a unit vector of a rotating coordinate system including a rotation axis of a rigid body, a rotation angle around the rotation axis, or a rotation center coordinate.
[0019]
Further, in the rigid body motion measuring method according to the present invention, a matrix component representing rotation in three rows and three columns and a matrix having a vector component in three rows and one column are calculated, and a unit vector of a rotating coordinate system including a rotation axis, a rotation axis Since the rotation angle of rotation and the coordinates of the rotation center are calculated, it is possible to quantitatively measure the change in relative rotational motion characterized by the functions of the two rigid bodies by tracking these rotational motion characteristic values.
[0020]
Furthermore, in the jaw movement measuring method of the present invention, the plurality of markers attached to the upper jaw of the subject and the lower jaw of the subject are reflective markers, and therefore can be measured in a general room.
[0021]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. FIG. 1 is an explanatory diagram of an actual use situation of a jaw movement measuring apparatus according to the present invention. A head frame 12 having three spherical markers 11 on the head of the subject 1 and a lower jaw marker tool 13 having three spherical markers 11 on the lower jaw are attached and fixed. Two first reflecting mirrors 15 are arranged on the measurement table 14 in such a direction that the head frame 12 and the lower jaw marker 13 are projected from both sides, and are sandwiched between the two first reflecting mirrors 15a and 15b. Two second reflecting mirrors 16 are placed so as to project the image projected on the reflecting mirror 15. One side of the two second reflecting mirrors 16a and 16b is in contact with each other, and the video camera 17 having, for example, 320 × 240 pixels is placed so that the contacted side is in the center of the field of view of the video camera 17. A signal cable 18 is connected from the video camera 17 to a computer 19.
[0022]
  FIG. 2 is a detailed view of the head frame 12 and the lower jaw marker 13, each of which includes three lightweight markers 11, for example, a blue marker made of a light material such as a spherical polystyrene having a diameter of 10 mm to 30 mm, Have These markers are fixed to the frame bodies 20 and 21 having rigidity such as a truss structure combining a rod-like or plate-like frame material made of a light material such as plastic with an adhesive or the like. The head frame 12 is fixedly attached to the frame body 20 with a band material 22 made of a flexible material such as cloth or plastic, and is formed into a shape that conforms to the head of the subject as a whole. In some strips, for example, Velcro(Registered trademark)It has a detachable fastening part 23 called by the name. The lower jaw marker tool 13 is fixedly attached to a part of the frame body 21 with a plate-like mounting plate 24 made of a light and rigid material such as metal, and a mouthpiece 25 is attached to the tip of the mounting plate 24. Is fixedly mounted.
[0023]
FIG. 3 is a top view showing the optical arrangement relationship of the first reflecting mirror 15, the second reflecting mirror 16, and the video camera 17. The images on the orthogonal OX and OY axes of the head frame 12 and the lower jaw marker 13 to which the marker 11 is fixed and fixed follow the optical path 26 indicated by the solid line and reach the video camera 17, and the image on the OY axis is the video camera. The first reflecting mirrors 15 a and 15 b and the second reflecting mirrors 16 a and 16 b are arranged so that the image on the left half of the field 17 and the image on the OX axis appear in the field of the right half of the video camera 17. This arrangement can be appropriately set according to the constraints such as the size of the subject and the size of the entire apparatus by designing the optical path 26 using the classical optical formula and the geometric formula. In the embodiment of the present invention, the two second reflecting mirrors 16a and 16b are orthogonal to each other and are also orthogonal to the OX axis and the OY axis, and the video camera 17 is connected to the OX from the intersection point O of the OX axis and the OY axis. It was placed under the condition of being placed on a line forming an angle of 45 degrees from the axis.
[0024]
FIG. 4 is a block diagram showing a hardware configuration of the computer 19. Control for controlling the entire system including an input unit 32 connected to a keyboard 31 and the like, a three-dimensional measuring device interface 33 connected to a three-dimensional measuring device 17 such as the video camera, and a measurement command of the three-dimensional measuring device 17. Unit 34, a memory unit 35 for storing data such as measured values and calculation results, an external storage device 36 connected when necessary, a calculation unit 37 for performing calculations, and displaying data such as calculation results on a CRT screen, plotter, etc. An output unit 39 for outputting to the device 38 is provided, and these are connected to the CPU 40 by a bus line.
[0025]
Next, the operation of the embodiment of the present invention will be described. First, as shown in FIG. 2, the subject 1 covers the head frame 12 having the three markers 11 over the head, and the frame body 20 and the band member 22 are stabilized along the head as shown in FIG. The head frame 12 is firmly fixed to the head using the portion 23. Since the head and the upper jaw can be regarded as an integral rigid body in terms of movement, it can be considered that the movement of the three markers 11 attached and fixed to the head frame 12 represents the movement of the upper jaw of the subject 1. Next, the mouthpiece 25 is firmly attached and fixed to the lower jaw of the subject 1, specifically, the lower gum with a dental instant adhesive. Therefore, it can be considered that the movement of the three markers 11 attached and fixed to the lower jaw marker tool 13 represents the lower jaw movement of the subject 1. The subject 1 with the head frame 12 and the lower jaw marker 13 ready is seated on a chair or the like toward the measuring table 14 on which the first reflecting mirror 15, the second reflecting mirror 16, and the video camera 17 are installed.
[0026]
Next, the principle of measuring the position coordinates of the marker 11 in the arrangement relationship of FIG. 3 is shown in FIG. The subject 1 sits in the first quadrant of the plane represented by the OX axis and the OY axis. The optical system shown in FIG. 3 uses a single video camera because the image on the OX axis and the image on the OY axis are projected to the right half and left half fields of view of the video camera 17 by the reflecting mirror, respectively. In operation, this is equivalent to installing the cameras C1 and C2 on the OX axis and the OY axis, respectively. FIG. 5A shows how the image appears when an object “black circle at the base of the arrow” is placed in the first quadrant. When the virtual camera C2 sees the “black circle at the base of the arrow” in the first quadrant, the intersection on the OY axis of the line connecting the C2 point and the “black circle at the base of the arrow” appears on the OY axis. Similarly, when the virtual camera C1 sees the “black circle at the base of the arrow” in the first quadrant, the intersection on the OX axis of the line connecting the C1 point and the “black circle at the base of the arrow” appears on the OX axis. . The point representing the black circle is now M, and its coordinates are (X₁, Y₁, Z₁), The coordinates x of the image on OX₁, Coordinate y of the image on the OY axis₁Is determined by the positional relationship between the points C1, C2 and M, and the coordinates of the images on the OX axis and the OY axis on the first reflecting mirrors 15a and 15b are the coordinates of the first reflecting mirrors 15a and 15b on the OX axis. , Determined by the angle with the OY axis. Similarly, the coordinates of the image reflected on the first reflecting mirrors 15a and 15b are the coordinates of the image reflected on the second reflecting mirrors 16a and 16b, and the coordinates of the images reflected on the second reflecting mirrors 16a and 16b are the coordinates x of the image reflected on the video camera 17._b, Y_bIs also determined by these relative angles. Therefore, the coordinates of M point (X₁, Y₁, Z₁) X₁, Y₁Is the coordinate x of the image captured by the video camera 17_b, Y_bIt is requested from. Here, although the positions C1 and C2 of the virtual camera are not known, a calibration object whose length is known in advance is placed in the first quadrant, and finally the length of the calibration object that is reflected on the video camera. By calculating and calibrating, it is possible to determine the coordinate conversion magnification of the entire optical system.
[0027]
M point coordinates (X₁, Y₁, Z₁Z)₁Is obtained from the relationship shown in FIG. Height coordinate Z of M point₁From the point of C2, x from the OY axis₁Copy the distant point on the OY axis. Z_L(L is given for convenience in the sense of the left side of the video camera). On the other hand, when the height coordinate of the same M point is seen from the C1 point, it is y from the OX axis.₁Copy the distant point on the OX axis. Z_R(R means the right side of the video camera) x₁And y₁Z is different_LAnd z_RCan be distinguished. x₁, Y₁Is known, so this z_LAnd z_RZ difference₁Can be requested.
[0028]
Based on the above-described measurement principle of the position coordinates of the marker, the computer 19 instructs the video camera 17 to take an image according to a program that causes the control unit 34, the memory unit 35, the calculation unit 37, etc. to execute a predetermined processing procedure. The captured data is taken in and processing such as calculation is performed. FIG. 6 shows a flowchart in the embodiment of the present invention.
[0029]
STEP 1 is a processing procedure for reading the marker coordinates of the lower jaw and the upper jaw with the camera. In the computer 19, 30 frames per second obtained by an image pickup device such as a CCD provided in the video camera 17 through a three-dimensional measuring instrument interface 33 such as a capture board having an AVI (audio video interface) according to a command from the control unit 34. The moving image of the subject is taken into the computer 19 for each frame, the position of the marker on the 320 * 240 pixel surface of each frame is recognized, and the computing unit 37 follows the coordinate measurement principle described in FIG. The three-dimensional position coordinates of the marker on the specimen are calculated, and the measured values of the lower and upper jaw marker coordinates are stored in the memory unit 35.
[0030]
STEP2 is a procedure for calculating the lower jaw specific point, the coordinates of the upper jaw specific point and the unit vector. That is, it is a processing procedure for calculating the three-dimensional six-degree-of-freedom of the three-dimensional coordinates and the three-dimensional rotation angle of a specific point having a specific positional relationship with the first rigid body and the second rigid body, respectively. First, the processing procedure for determining a specific point and a unit vector is shown in FIG. Considering a plane A defined by three markers attached to the lower jaw marker 13, one marker is a specific point L_OAnd that specific point is the origin. Next, the direction including one of the other markers is defined as the X axis, and the position occupied by that marker on the X axis is a point L._XAs a specific point L on the plane A_O, Line segment L_OL_XThe Y axis is taken in the direction orthogonal to the specific point L on the Y axis._ODistance from is line segment L_OL_XA position equal to the length of the point L_YAnd Furthermore, a specific point L in the direction perpendicular to the plane A_OTake the Z-axis in the direction passing through and a specific point L on the Z-axis_ODistance from is line segment L_OL_X, L_OL_YA position equal to the length of the point L_ZAnd In this way, a specific point L of the coordinate system having a specific positional relationship with the lower jaw_OAnd a specific point L_OUnit vector L with origin at_OL_X, L_OL_Y, L_OL_ZDetermine. The same applies to the upper jaw.
[0031]
Next, this specific point L_OConversion of the position coordinate when the position coordinate of is measured from the coordinate system of the video camera 17_LCIs calculated by equation (1).
[Expression 1]

Where T_LCRepresents the conversion from the coordinate system having a specific positional relationship with the lower jaw to the coordinate system of the video camera 17, C_X, C_Y, C_ZIs the position coordinate seen from the coordinate system of the video camera 17, L_X, L_Y, L_ZIs the position coordinate seen from the coordinate system with a specific positional relationship with the lower jaw, G_CLIs a 3-by-3 matrix representing the rotational transformation of the unit vector, a_CLIs a vector with 3 rows and 1 column. L now_X, L_Y, L_ZAre zero because they are the origin. The specific point L is calculated by the calculation of the equation (1)._OThe three-dimensional coordinates and the three-dimensional rotation angle are calculated.
[0032]
Similarly, a specific point U of the coordinate system having a specific positional relationship with the upper jaw_O, Specific point U_OUnit vector U with origin_OU_X, U_OU_Y, U_OU_ZIs determined. Next, this specific point U_OIs converted to a position coordinate when measured from the coordinate system of the video camera 17_UCIs calculated by equation (2).
[Expression 2]

The meaning of the symbols is the same as in Equation 1.
[0033]
That is, in this processing procedure, the computer 19 reads out the marker coordinate measurement values of the lower jaw and the upper jaw from the memory unit 35, and the calculation unit 37 determines specific points and unit vectors respectively having a specific positional relationship with the lower jaw and the upper jaw. The equations (1) and (2) are calculated, and the calculated data is stored in the memory unit 35.
[0034]
STEP 3 is a processing procedure for converting the coordinates and unit vector of the upper jaw specific point as a reference. The specific point L obtained by the calculation of the expressions (1) and (2) of STEP 2_OAnd specific point U_OThe specific point U having a specific positional relationship with the upper jaw from the position coordinates measured from the coordinate system of the video camera 17_OA specific point L that has a specific positional relationship with the lower jaw, based on the three-dimensional coordinates and unit vector_OConvert 3D coordinates and 3D rotation angle.
[0035]
In general, the conversion from A to B is T_AB, Convert B to C_BC, Conversion from C to A_CAThen, equation (3) holds between these three.
[Equation 3]
T_CAoT_BCoT_AB= 1
T_BC= T_CA ^-1oT_AB ^-1= T_CA ^-1oT_BA... (3)
Here, for example, T_BCoT_ABT_ABConvert to T_BCIt represents that it was given. Therefore, if A is a coordinate system of a video camera, B is a coordinate system having a specific positional relationship with the lower jaw, and C is a coordinate system having a specific positional relationship with the upper jaw, a specific point L having a specific positional relationship with the lower jaw._O3D coordinates, 3D rotation angle, specific point U with a specific positional relationship with the upper jaw_OConversion T for conversion based on 3D coordinates and unit vector_LUIs the T in equation (1)_LC, T in equation (2)_UCIs calculated by the equation (4).
[Expression 4]
T_LU= T_UC ^-1oT_LC                        ... (4)
The T thus obtained_LUEven if the upper jaw and the lower jaw move relative to each other, the movement of the lower jaw can be captured with reference to the upper jaw. Therefore, unless otherwise specified, the lower jaw movement will be considered.
[0036]
That is, this processing procedure is performed in the computer 19 by storing the three-dimensional coordinates and the three-dimensional rotation angle of the specific point having a specific positional relationship with the lower jaw and the specific point having a specific positional relationship with the upper jaw, which are stored in the memory unit 35. 3D coordinates and 3D rotation angle data are read out, and the calculation unit 37 performs coordinate conversion of the 3D coordinates and 3D rotation angle data of a specific point on the lower jaw with reference to a coordinate system fixed to the upper jaw. . The coordinate-converted data is stored in the memory unit 35.
[0037]
STEP 4 determines whether or not a relative motion is being performed. If the relative motion is being performed, STEP 1 to STEP 3 are repeated. When the relative motion is completed and data measurement is not necessary, the processing from STEP 1 to STEP 3 is terminated. Proceed to the next STEP5. For example, when measuring a series of relative motions with moving image data of 300 frames, the processing from STEP 1 to STEP 3 is completed in about 10 seconds.
[0038]
STEP 5 is a matrix calculation processing procedure indicating a change in the movement position. In general, motion in space is a combination of rotation and translation. If a coordinate system in the space is defined, a point in the space can be expressed as a three-dimensional vector, so that the existing space point is M and x is the vector. When the point M is moved by movement, the coordinates after the movement are expressed as Gx + a using a matrix G representing rotation and a vector a. In order to show this as a matrix product, it is expressed as equation (5) as four rows and one column obtained by adding another row 1 to x in three rows and one column.
[Equation 5]

That is, the motion of the point M can be expressed by a matrix of 4 rows and 4 columns including a matrix component G of 3 rows and 3 columns representing rotation and a vector a which is a matrix component of 3 rows and 1 column.
[0039]
Now the specific point L of the lower jaw_OA 4-by-4 matrix representing the first motion position for H_1UAnd a 4-by-4 matrix representing the second motion position is H_2UThen, these are the specific points U of the upper jaw from the first movement position and the second movement position, respectively._OEquivalent to conversion to Using the relationship of Equation (3), the specific point L of the lower jaw_OTransformation H representing the movement from the first movement position to the second movement position₁₂Is represented by Formula (6).
[Formula 6]
H₁₂= H_2U ^-1oH_1U                          ... (6)
[0040]
That is, this processing procedure is performed by the computer 19 according to the equation (4) T stored in the memory unit 35._LUThe data in the first motion state and the second motion state are read from the data of_1U, H_2UAs a result of calculating the expression (6) in the calculation unit 37, the movement position of the specific point from the first movement position to the second movement position on the basis of the coordinate system fixed to the first rigid body A motion matrix representing the change is calculated, and the result is stored in the memory unit 35.
[0041]
STEP 6 is a processing procedure for calculating a unit vector of the rotating coordinate system. Since the unit vector in the direction of the rotation axis passing through the center of rotation is an eigenvector having the eigenvalue 1 of the matrix G representing rotation, the matrix H of 4 rows and 4 columns calculated by Expression (6) is used.₁₂For the matrix component G of 3 rows and 3 columns representing the rotation of the eigenvector, the eigenvector whose eigenvalue is 1 is calculated using a well-known sweeping method or the like to determine the unit vector in the direction of the rotation axis, and the remaining two axes The unit vector is also calculated in the process.
[0042]
That is, this processing procedure is performed by a four-by-four matrix H stored in the memory unit 35 in the computer 19.₁₂In the arithmetic unit 37, arithmetic processing for obtaining an eigenvector of the eigenvalue 1 is performed on a matrix of three rows and three columns representing the rotation, and the result is stored in the memory unit 35.
[0043]
STEP 7 is a processing procedure for calculating the rotation angle. It is well known that if the unit vector of the rotating coordinate system obtained in STEP 6 is P, the relationship is expressed by equation (7).
[Expression 7]

Here, θ represents a rotation angle around the rotation axis of the rigid body. That is, in the computer 19, H stored in the memory unit 35 is stored.₁₂And the eigenvector P are read out, the equation (7) is calculated, and the result is stored in the memory unit 35.
[0044]
STEP 8 is a processing procedure for calculating the rotation center coordinates. A specific point L having a specific positional relationship with the lower jaw_OMotion matrix H representing the motion from the first motion position to the second motion position₁₂As shown in the equation (8), a translational component b of the center of rotation in the direction of the rotation axis is obtained when a is viewed in the rotational coordinate system.₁And the coordinate movement component b by the rotation angle θ around the rotation center₀It is divided into.
[Equation 8]

Where a is 3 rows and 1 column, b₀Is two rows and one column, b₁Is a scalar quantity. b₀Is a specific point L from the center of rotation._OThe radius of rotation to c₀Then, there is a relationship of Expression (9).
[Equation 9]
b₀= C₀-G * c₀
c₀= (IG)^-1* B₀                      ... (9)
Here, I is a unit matrix. This c₀And specific point L_OThe position coordinates of the rotation center can be calculated from the position coordinates. That is, in the computer 19, the H stored in the memory unit 35 is stored.₁₂, And the calculation unit 37 calculates equations (8) and (9) for the vector component a, calculates the rotation center coordinates, and stores the result in the memory unit 35.
[0045]
STEP 9 determines whether or not all of the processing procedures of STEP 5 to STEP 8 have been completed for the series of relative motion data stored in the memory unit 35. If not, the processing procedure of ending STEP 1 to STEP 3 is terminated. If the process is repeated, the process proceeds to the next STEP 10. For example, when calculating a series of relative motions from 300 frames of moving image data, the processing from STEP 1 to STEP 3 is completed in about five minutes.
[0046]
STEP 10 is a display processing procedure. The unit vector of the rotation coordinate system including the rotation axis, the rotation angle around the rotation axis, and at least one rotational motion characteristic value of the rotation center coordinate are displayed. That is, in the computer 19, these rotational motion characteristic values are read from the memory unit 35 and displayed on a display device 38 such as a CRT screen or a plotter of the computer via the output unit 39.
[0047]
FIG. 8 is an example of measurement results in the embodiment of the present invention. FIG. 8 (a) shows a healthy person, FIG. 8 (b) shows a patient with a click symptom, and gradually opens the lower jaw with respect to the upper jaw. Close movement is performed, time (image frame number) is taken on the horizontal axis, and the rotation angle, rotation center position coordinate, rotation unit vector, and rotation center translation with respect to the rotation axis of the lower jaw every moment on the vertical axis. It represents the quantity. When FIG. 8A is compared with FIG. 8B, the points indicated as (1), (2), and (3) in the figure are different. At these motion positions, it can be clearly seen that the center of rotation has moved and that the unit vectors have also changed. That is, at the points (1) and (3), it can be seen that when the engagement between the lower jaw and the upper jaw starts and ends, there is a meshing phase abnormality in which the upper jaw and the lower jaw do not normally contact in the engagement, (2) It can be seen that there is a discontinuity in the jaw opening and closing movement, and there is a movement phase abnormality in which a “click” sound is sometimes observed. In this way, the relative movements characterized by the functions of the two rigid bodies such as the upper jaw and lower jaw meshing and opening and closing are quantitatively expressed as rotational motion characteristic values such as rotation angle, rotation center coordinates, unit vector, and rotation center translation. Can be measured and the results can be displayed.
[0048]
In the embodiment of the present invention, the mandibular movement has been described in detail, but the present invention can be implemented with respect to the relative movement of two rigid bodies characterized by the rotational movement function of joints such as knees, arms, and fingers. In this case, the subject is not limited to a human being or a living body other than a human being, and the present invention can also be implemented for a robot. The present invention can also be implemented for measuring the rigid body motion between the first rigid body and the second rigid body that move relative to each other, such as a mechanism of a part of the mechanical device.
[0049]
As for the display, the present invention can also be implemented by further performing coordinate transformation and displaying the measured values in a coordinate system that is easy to observe.
[0050]
Of the flowcharts in the embodiment of the present invention, STEP 1 to STEP 10 are made one program, or STEP 1 to STEP 3 and STEP 4 and later are separated into two programs to implement the present invention. Can do.
[0051]
In addition to the embodiment of the present invention, the size, shape, color, etc. of the marker can be implemented by changing the reflective marker within the range of design matters in accordance with each embodiment. In addition to the embodiment of the present invention, the position coordinate measurement principle can be implemented by a plurality of non-contact and contact three-dimensional measuring instruments.
[0052]
【The invention's effect】
In the rigid body motion measuring method according to the present invention, a plurality of markers are attached and fixed to each of the first rigid body and the second rigid body that move relative to each other, and the three-dimensional coordinates of the plurality of markers during the relative motion are measured. Calculate the 3D coordinates and 3D rotation angle of a specific point with a specific positional relationship with the second rigid body based on the coordinate system fixed to the first rigid body, and the first motion position in relative motion The first movement position of the specific point based on the coordinate system fixed to the first rigid body from the two three-dimensional six-degree-of-freedom calculation results of the specific point obtained at the second movement position. A motion matrix calculation step for calculating a matrix representing a change in the movement position from the first movement position to the second movement position, and converting the movement matrix obtained by the calculation into a rotation movement matrix based on a rotational coordinate system of a rigid body, Rotational coordinate system including the rotation axis as the rotational motion characteristic value of the rigid body By calculating the unit vector, the rotation angle around the rotation axis, and the rotation center coordinates, tracking these rotational motion characteristic values quantitatively changes the relative rotational motion characterized by the functions of the two rigid bodies. It was possible to measure.
[0053]
Furthermore, in the jaw movement measuring method according to the present invention, the plurality of markers attached to the upper jaw of the subject and the lower jaw of the subject are reflective markers, so that measurement in a general room is possible.
[Brief description of the drawings]
FIG. 1 is an explanatory diagram of a use situation of a jaw movement measuring device according to an embodiment of the present invention
It is.
FIG. 2 is a detailed view of a head frame and a lower jaw marker tool in the embodiment of the present invention.
FIG. 3 is a layout diagram of an optical system according to an embodiment of the present invention.
FIG. 4 is a block diagram of a computer according to the embodiment of the present invention.
FIG. 5 is a diagram illustrating the principle of measuring the position coordinates of a marker in the embodiment of the present invention.
FIG. 6 is a flowchart in the embodiment of the present invention.
FIG. 7 is an explanatory diagram of definitions of specific points and unit vectors in the embodiment of the present invention.
FIG. 8 is an example of measurement results in the embodiment of the present invention, where (a) is for a healthy person and (b) is for a person with a “click” symptom.
FIG. 9 is a principle view of a conventional mandibular movement measuring device.
FIG. 10 is an example of a measurement result of a change in coordinates due to opening and closing of the jaw in the conventional example.
[Explanation of symbols]
1 subject, 2 lower jaw, 3 upper jaw, 4 facebow (L), 5 facebow (U), 6 LED, 7 coordinate system Σ_L, 8 coordinate system Σ_U, 9 Camera coordinate system Σ, 10 Coordinate system Σ_H, 11 Marker, 12 Head frame, 13 Mandibular marker tool, 14 Measuring table, 15, 15a, 15b First reflecting mirror, 16, 16a, 16b Second reflecting mirror, 17 Video camera (three-dimensional measuring device), 18 Signal cable , 19 Computer, 20, 21 Frame body, 22 Band material, 23 Tightening part, 24 Mounting plate, 25 Mouthpiece, 26 Optical path, 31 Keyboard, 32 input part, 33 CMM interface, 34 Control part, 35 Memory Unit, 36 external storage device, 37 calculation unit, 38 display device, 39 output unit.

Claims (12)

A three-dimensional measuring step of measuring the three-dimensional coordinates of the plurality of markers in relative movement, which are attached and fixed to the first rigid body and the second rigid body, which are relatively moved relative to each other, with a three-dimensional measuring device; Calculate the 3D coordinates and 3D rotation angle of a specific point that has a specific positional relationship with the second rigid body based on the coordinate system that is fixed to the first rigid body In a rigid body motion measurement method having a three-dimensional six-degree-of-freedom calculation step that is calculated by means , two three-dimensional six points of the specific point obtained at a first motion position and a second motion position during relative motion are obtained. Based on the result of calculating the degree of freedom, a calculation means calculates a matrix representing a change in the movement position of the specific point from the first movement position to the second movement position with reference to the coordinate system fixed to the first rigid body. The motion matrix calculation process and the above calculation The obtained motion matrix is converted into a rotational motion matrix based on the rotational coordinate system of the rigid body, and at least one of the unit vector of the rotational coordinate system including the rotational axis, the rotational angle around the rotational axis, or the rotational center coordinate for the second rigid body. A rigid body motion measuring method comprising a rotational motion calculation step of calculating two rotational motion characteristic values by a calculation means . 2. The rigid body motion measuring method according to claim 1, wherein the motion matrix computing step computes a matrix having a matrix component representing a rotation of three rows and three columns and a matrix having a vector component of three rows and one column by a computing means. Rigid body motion measurement method.   A plurality of markers respectively attached and fixed to the first rigid body and the second rigid body that move relative to each other; a three-dimensional measuring device that measures the three-dimensional coordinates of the plurality of markers during the relative movement; Calculate the 3D coordinates and 3D rotation angle of a specific point that has a specific positional relationship with the second rigid body based on the coordinate system that is fixed to the first rigid body Two-dimensional six-degree-of-freedom calculation of the specific point obtained at the first movement position and the second movement position in the relative movement From the results, a motion matrix computing means for computing a matrix representing a change in motion position from the first motion position of the specific point to the second motion position, with reference to the coordinate system fixed to the first rigid body, The motion matrix obtained by the above calculation is used to rotate the rigid body. Rotation that converts to the rotational system matrix of the reference system standard and calculates at least one rotational motion characteristic value of the rotation vector around the rotational axis or the rotational center coordinate of the rotational coordinate system including the rotational axis of the second rigid body A rigid body motion measuring device comprising motion calculation means.   4. The rigid body motion measuring apparatus according to claim 3, wherein the motion matrix computing means computes a matrix having a matrix component representing rotation in three rows and three columns and a vector component having three rows and one column. Motion measurement device.   A computer that measures the movement of a rigid body, and a three-dimensional measuring instrument that measures the three-dimensional coordinates of a plurality of markers attached and fixed to the first rigid body and the second rigid body, which move relative to each other by the control unit. Commanding and reading the three-dimensional coordinate measurement value stored in the memory unit by a measurement processing procedure for taking in and storing the three-dimensional coordinate measurement value in relative motion into the memory unit of the computer and the calculation unit of the computer, Executes a 3D six-degree-of-freedom calculation procedure that calculates the 3D coordinates and 3D rotation angle of a specific point with a specific positional relationship with the second rigid body based on the coordinate system fixed to the first rigid body In the rigid body motion measurement program, two of the specific points obtained at the first motion position and the second motion position during the relative motion are further calculated by the computing unit of the computer. Calculate a matrix representing the change in the movement position of the specific point from the first movement position to the second movement position based on the coordinate system fixed to the first rigid body from the three-dimensional six-degree-of-freedom calculation result. The motion matrix calculation processing procedure and the motion matrix obtained by the above calculation are converted into a rotation motion matrix based on the rotation coordinate system of the rigid body, and the unit vector or rotation axis of the rotation coordinate system including the rotation axis of the second rigid body A rigid body motion measurement program for executing a rotational motion calculation processing procedure for calculating at least one rotational motion characteristic value of a rotation angle of rotation or a central coordinate of rotation.   6. The rigid body motion measurement program according to claim 5, wherein the motion matrix computation processing procedure computes a matrix having a matrix component representing rotation in three rows and three columns and a matrix having vector components in three rows and one column. Rigid body motion measurement program. In rigid body motion measuring method according to claim 1 or claim 2, three-dimensional measurement process, the first rigid and the upper jaw of the subject, the second rigid as mandible of the subject, the mutually relative movement jaw tracking method characterized that you measured by three-dimensional measuring device three-dimensional coordinates of the plurality of markers each in relative motion, which is mounted fixed to the lower jaw of the upper jaw and the object of the subject to be.   5. The rigid body motion measuring device according to claim 3, wherein the first rigid body is the upper jaw of the subject and the second rigid body is the lower jaw of the subject.   7. The rigid body motion measurement program according to claim 5, wherein the first rigid body is the upper jaw of the subject, and the second rigid body is the lower jaw of the subject. In rigid body motion measuring method according to claim 1 or claim 2, three-dimensional measurement process, the first rigid and the upper jaw of the subject, the second rigid with the lower jaw of the subject, the upper jaw of the subject And a plurality of markers attached to the lower jaw of the subject as reflection type markers , and the three-dimensional of the plurality of markers in relative motion attached and fixed to the upper jaw of the subject and the lower jaw of the subject that move relative to each other, respectively jaw tracking method characterized that you measured by three-dimensional measuring device coordinates.   5. The rigid body motion measuring apparatus according to claim 3, wherein the first rigid body is the upper jaw of the subject, the second rigid body is the lower jaw of the subject, and the upper jaw and the lower jaw of the subject. The jaw movement measuring device characterized in that the plurality of markers attached to the are reflex type markers.   7. The rigid body motion measurement program according to claim 5, wherein the first rigid body is the upper jaw of the subject, the second rigid body is the lower jaw of the subject, and the upper jaw and the lower jaw of the subject. The jaw movement measuring program characterized in that the plurality of markers attached to the are reflex markers.

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