SU1427335A1 - Device for measuring the components of quaternion - Google Patents

Abstract

The invention relates to automation and computer technology and can be used to measure the components of a quaternion determining the relative spatial arrangement of the moving elements of a multi-stage mechanical suspension. The purpose of the invention is to expand the functionality. The device for measuring the components of the quaternion contains a sine-spinning rotating transformer 1, the first 2 and second 3 anapic-digital converters, the shift register 4, the digital adder 5, the digital subtractor 6, the first 7 block of constants, the multiplication unit 8, the second block 9 constants, unit 10 for computing the square root, switch 11, generator 12 clock pulses. The purpose of the invention is achieved by the introduction of elements and blocks 4-11. 1 il. (L

Description

Uma agffffff & ma

ffQM

4i -vl

WITH

from cd

,; one"

The invention relates to automation and computer technology and can be used to measure the components of a quaternion determining the relative spatial arrangement of the moving elements of a multi-stage mechanical suspension.

. The purpose of the invention is to expand the functionality.

The basis for the operation of a device is the property that the normalized quaternion arc Ld, as a function of time t, can generally be represented by the well-known trigonometric formula

La () Aa (coso ((t) -t-l sino (. (T) y (1

where is aacoso ((t) and (t}

{Components ; waternion-dupi; unit vector coinciding with the vector of the quaternion.

At the same time, the vector part of the corresponding quaternion, associated with the mechanical suspension element, is either a priori known (fixed in. Inertial 30 basis) or located in a known non-suspended (a priori known) plane, 1-shee in a rotating plane, etc.

Any quaternion arc Lb. (Ags) 35 and the corresponding quaternion operator of rotation Ag. (0pj are in the following relationship:

L to (S оС ()

La (.oR) La (co-5

) (2-)

25 s;

40

The drawing shows the functional diagram of the device for. measuring quaternion components.

A device for measuring the components of a quaternion contains a sine-cosine rotating transformer I, first 2 and second 3 analog-digital converters, shift register 4, digital adder 5, digital subtractor 6, first block 7 of constants, block 8 multiplication, second block 9 of constants, block 10 square root computing, switch 1, 12 clock pulse generator.

The device works as follows.

During the rotation of the sine-cosine rotary transformer .1. beep

0

five

its windings are fed to the inputs of analog-to-digital converters 2, 3, where they are converted into a digital form. The codes at the outputs of the first and second analog-to-digital converters are components of the arc quaternion, with the binary code corresponding to the voltage from the sine

The windings will determine the scalar part 1 of the innernion-arc, and the code corresponding to the voltage from the cosine winding will determine its vector part. Thus, reading information from

5 of the first and second outputs of the device, it is possible to digitally determine the quaternion arc by the formula

,;) Go (nT) + i5Gsy (nT) j.

0 where D (q5 quaternion arc;

PT - discrete time; 5 Gjj - scalar and vector components.

5 From the output of the second analog-to-digital converter, the code also enters a group of bypasses of the shift register 4 and the digital calculator 6. From the output of the shift register, the signal delayed per clock of the clock pulse generator is fed to the input of the digital adder. The second group of inputs of digital adders 5 and subtractor 6-enters a single constant from the first block of 7 constants. The signals from the outputs of the digital adder and subtractor with a shift in time arrive at the first group of inputs of the multiplication unit 8, where it is multiplied by the constant 0.5 stored in the second block 9 of the constants. The result of the multiplication is fed to the input of the square-root computing unit 10, at the output of which the components c are alternately generated; quaternion operator of rotation, distributed switches 1 1 to the third and fourth outputs of the device. Thus, by reading information from these outputs, it is possible to digitally determine the quaternion-operator of rotation by the formula

Ac (orc5 ssusor; + (or), where Gcc :: f (OP) ± So, 5 (H-Gc7),. 5 Gcs: fcoP) tVO, 5 (l-Gcy),

respectively, the scalar and vector components of the quaternion operator of rotation.

0

0

Claims (1)

Invention Formula A device for measuring the components of a quaternion, containing the first and second analog-digital converters, a multiplication unit, a clock generator, connected by an output to the clock inputs of the analog-digital converters and a control input of the multiplication unit, in order to expand the functional capabilities, introduced sine-cosine rotating: transformer, shift register, digital adder, digital subtractor, first and second blocks of constants, square root calculation unit and switch, blue ny sine and cosine outputs kosinusno--th rotary transformer respectively through first and second analog-to-digital converters are connected to the first and second groups of outputs of the device, Informational oynye vzhody second analog-to-digital converter connected to Vågå the first group of information inputs of the digital adder, the second group of information inputs of the digital subtractor and the digital adder are connected to the outputs of the first block of constants, the information outputs of the digital adder and digital subtractor are connected to the first group of information inputs of the multiplication unit, the second group of information inputs of which are connected to the outputs of the second block of constants , and information outputs are connected to the input of a square root calculation block, the output of which is connected to information inputs of the mutator first and second groups of information whose outputs are the third and fourth groups of device outputs, the output of the clock generator is connected to the clock inputs of the shift register and the control inputs of the first and second blocks of constants, multiplication unit, square root computing unit and switch.