JPS5918752B2 - square root calculator - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a square root calculator that performs a square root calculation of an input signal.

An object of the present invention is to provide a highly accurate and compact device.

FIG. 1 is a detailed explanatory diagram of the present invention.

In FIG. 1, A is a balanced beam.

The balanced beam A is composed of a first beam A1 and a second beam A2.

The first beam A1 is pivotally supported at one end and rotated around the other end.

Further, the right end of the second beam A2 is connected to the first beam A1, and the left end is made to be movable on the reference line XX passing through the pivot point 0.

Now, when the left end of the second beam A2 moves from Xl to x2, the connection point is rotationally displaced from yl to y2.

Here, the lengths of the first and second beams A, A2 are R
, L, and both beams A1. If the angles between A2 and the X-X line are θ and α, the following relational expression holds true.

L sin a=R sin θ ---
--・(1) Also, X2X1"X13'l X2C""C)'1x2x1
=x, X1yl=I, f x2C=LcosαC
Since y1=R-Rcosθ=R(1-cosθ), x +L-L cos a=R(1-cosθ) −
-----・(2) (1) and (2) are squared and added.

(1) Squared R25in2θ−L2sinα=0 ・・・・・
...(G) Square of formula (2) ((X+L) R(1-cosθ))2-L2CO
52α=O...7) (g)+(9) R25in2θ-L2Sin2α+(x+L)2-2R
(x+L)(1-cosθ)+R”(1-cosθ)2
-Lcos α=0 Rearranging this equation, x2+2xL-2R(1-cosθ)(x+L R)
""0......(C) "-" 5in2θ+CO52θ21 On the other hand, the expansion formula for cosθ is as follows.

θ2 θ4 θ6 cosθ=1−−10−10− 246 When θ is small, the third term and below can be ignored, so 1− CO5θ=θ2/2, so substituting this into equation (0) , 2x L+
, x/2 θ2=-・□ Rx+L-R O=-7x)] Four feet (3) Rx+L-R In equation (3), if X is sufficiently small compared to L and (L-R), θ =kJ7・・・・・・・・・
-(4) However, k: is a constant, and θ is proportional to the square root value of X.

For example, when R = 50 dragons and L = 100 gm, (3
) The difference between the calculated value in equation (4) and the calculated value in equation (4), which is an ideal square root curve, is as shown in the table below.

That is, when θ is within 6 degrees, the error can be set to o, o5% or less.

The present invention provides a square root calculator that performs a square root calculation using the above principle.

FIG. 2 is an explanatory diagram of the configuration of an embodiment of the present invention.

In Figure 2, 1 is the input bellows, 2 is the feedback bellows, 3
is a balanced beam.

As described above, the balance beam 3 has the first and second arm frames 31 and 32, and these arm frames are connected by the connecting portion 33.

The connecting portion 33 extends upward, and the two arm frames 3
1 and 32 form the reference line and the inclination angles θ and α.

Reference numeral 4 denotes a movable plate arranged in a direction intersecting the balance beam 3.

The movable plate 4 is made up of a first and a second movable piece 41 and 42, and both of these rotary pieces 41 and 42 are supported on a coaxial fulcrum 43, so that the other end can be displaced.

Further, a middle portion of the second movable piece 42 is connected to an end portion of the second armrest 32.

Then, the movable end of the input bellows 1 is fixed to the movable piece 41,
A return bellows 2 is attached to the arm frame 31.

11 is a span adjustment spring, and 12 is a zero adjustment spring.

5 is a nozzle flapper mechanism. Nozzle flapper mechanism 5
The nozzle 51 is attached to the movable piece 41, and the nozzle 51 is attached to the movable piece 42.
Opposing the flapper consisting of.

6 is a pneumatic amplifier that amplifies the back pressure of the nozzle 51.

r is the restriction, Al6 is the supply air pressure, Pi is the input pressure, and Po is the output pressure.

In the device having such a configuration, when the input air pressure Pi introduced into the bellows 1 increases, the movable piece 41 rotates around the fulcrum 43.

When the movable piece 41 rotates, the space between the nozzle 51 and the flapper 52 becomes narrower, and the nozzle back pressure increases.

The increased nozzle back pressure is amplified by the amplifier 6 and fed back to the bellows 2, which rotates the first armrest 31 counterclockwise to increase the inclination angle θ.

As the first arm rod 31 rotates, the connection point 33 is displaced, and the flapper 52 is separated from the nozzle 51.

Further, when the human pressure Pi decreases, the nozzle back pressure decreases, contrary to the above, and θ becomes smaller to reach equilibrium.

In this way, the balanced beam 3 is tilted in accordance with the magnitude of the input signal Pi and brought to rest in equilibrium at a new position.

Therefore, the relationships expressed by the aforementioned equations α1) to (4) are established between the displacement amount X of the second arm stick 32, that is, the movable plate 4, and the angle θ formed by the first arm stick 31.

Therefore, the air pressure calculation signal Po proportional to the square root value of the input signal Pi can be extracted from the output terminal out.

FIG. 3 is an explanatory diagram of the configuration of an apparatus according to an embodiment of the present invention, and FIG. 4 is a left side view thereof.

In FIGS. 3 and 4, B is a substrate.

The substrate B is formed into a substantially L-shape including a holding portion B0, a columnar portion B2, a side surface portion B3, and a flat portion B4 that protrude toward the side.

B5 is a through hole that penetrates the columnar portion B2 in the horizontal direction.

1 to 6 are the same elements as already explained in FIG. 2, and the same symbols are used.

Then, the input bellows 1 is attached to the side part B3, and the return bellows 2
is attached to the flat part B4.

The balance beam 3 and the movable plate 4 attached to the substrate B are shown in FIG.

The balance beam 3 includes an arm frame 32, a U-shaped arm frame 31 that surrounds the arm frame 32 on the opposite side and is connected to the base side and supported so as to be able to be displaced, and this arm frame 31 is made independent of the second arm frame 32. It consists of a mounting plate 34 for coupling to the return bellows 2.

Reference numeral 35 denotes a flexible portion which is cut into a thin spring plate shape by slitting and is intended to allow this portion to be freely displaced.

36 is a patch plate on the opposite side of the arm frame 31, 37 is the second arm bar 32
It is an extension board.

The extension plate 37 passes through the hole B5 of the substrate B. 38 is arm frame 3
a hole 39 for fixing the open end of 1 to the columnar part B2;
is a hole into which the upper end of the span adjustment spring 11 is engaged.

The movable plate 4 made up of a first movable piece 41 and a second movable piece 42 as shown in FIG. 5 is used here.

Reference numeral 45 denotes a flexible portion formed on this movable plate 4, which is made in the same manner as the one described above, and constitutes the fulcrum 43.

Stoppers 13 and 14 are attached to the board B, and restrict the movement range of the movable piece 41 and the arm frame 31, respectively.

15 is a pillar on which the lower end of the spring 11 is hooked.

16 is a rotary knob. When the knob 16 is turned, the zero adjustment spring 12
The initial tension of can be changed to perform zero adjustment.

Note that the pneumatic amplifier 6 is located on the back side of the board B (bottom side in Fig. 3).
It is attached via a gasket, and the air circuit is automatically connected by fixing it.

Since the apparatus shown in FIGS. 3 to 5 operates in the same manner as the apparatus shown in FIG. 2, a description of its operation will be omitted.

According to the present invention described above, the following effects can be expected.

(1) In the conventional force balance mechanism of this type of arithmetic unit, janθ
There is something that uses .

Since such an apparatus uses an approximation equation of jan θ-θ, there is a problem in that a basic error occurs.

For example, when the angle θ is 6 degrees, the error reaches 0.14%.

On the other hand, in the present invention, as is clear from the table in Section 4 above, even when θ is selected to be 6 degrees, the error is within 0.05%, and the accuracy can be almost tripled.

(2) An L-shaped lever mechanism is constructed by combining a balance beam and a movable plate arranged in a direction crossing the balance beam, and an input bellow and a return bellow are arranged and surrounded inside this lever mechanism. Therefore, the entire device can be made small and compact.

Therefore, according to the present invention, it is possible to provide a small and compact square root calculation unit with high accuracy.

[Brief explanation of the drawing]

Fig. 1 is a detailed explanatory diagram of the present invention, Fig. 2 is an explanatory diagram of the configuration of an embodiment of the invention, Fig. 3 is a side view of the apparatus according to the embodiment of the invention, Fig. 4 is a left side view thereof, and Fig. 5 FIG. 3 is an explanatory diagram of a balanced beam used in the apparatus of FIG. A or 3...Balanced beam, 1...Input bellows, 2...Return bellows, 4...
Movable plate, 5... Nozzle flapper mechanism.

Claims (1)

[Scope of Claims] 1. A first arm rod whose one end is pivotally supported and whose other end is rotatably deflected around this pivot point; a balance beam configured with a second arm bar that is displaced on a reference line passing through a fulcrum, the lengths of the first arm bar and the second arm bar being R and L; A square root calculator that utilizes the principle of equation (3) derived from equations (1) and (2) below, where the angles formed by the armrest and the reference line are θ and α. L sinα=Rsinθ ・・・・・・・・・
・・・・・・・・・(1)x+L−Lcosα:R(1−c
osθ)+3°(2)θ=f】■”7(3) Rx+L-R A balanced beam configured of a first arm stick that is deflected, and a second arm stick that is connected to the deflected portion of the first arm stick and that is displaced on a reference plane whose other end side passes through the pivot point; A first member disposed parallel to the direction intersecting the balanced beam and having one end coaxially supported.
and a second movable piece, a nozzle flapper mechanism disposed between the two rotating pieces, an input bellow connected to the movable plate, and a return bellow connected to the first arm rod. A square root calculator consisting of and.