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# Control of Joint Angles

IP.com Disclosure Number: IPCOM000116651D
Original Publication Date: 1995-Oct-01
Included in the Prior Art Database: 2005-Mar-31
Document File: 2 page(s) / 38K

IBM

## Related People

Nakayama, Y: AUTHOR

## Abstract

Disclosed is a method for adjusting the angle of a joint with three degrees of freedom, such as that of a robotarm or an articulated figure in computer graphics. The orientation of a jointed arm is determined by two parameters, and thus there can be only one singular point among all the orientations of the arm. A sphere is projected onto a circle so that the orientation can be specified on a single panel.

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Control of Joint Angles

Disclosed is a method for adjusting the angle of a joint with
three degrees of freedom, such as that of a robotarm or an
articulated figure in computer graphics.  The orientation of a
jointed arm is determined by two parameters, and thus there can be
only one singular point among all the orientations of the arm.  A
sphere is projected onto a circle so that the orientation can be
specified on a single panel.

When x and y are parameters that determine the orientation of
the arm and &theta.  is a parameter that determines the rotation of
the arm, the rotation matrix of the joint is given by the formula:
T = R(x,y,0) % R(0,0, phi )
= left lparen <cos theta + t x sup 2 > cvabove < t x y >
cvabove < s y >
< t x y > cvabove < cos theta + t y sup 2 >
cvabove < - s x >
< - s y > cvabove < s x > cvabove < cos theta >
right rparen
left lparen < cos phi > cvabove < sin phi > cvabove 0
< - sin phi > cvabove < cos phi > cvabove 0
0 cvabove 0 cvabove 1
right rparen
where theta = sqrt < x sup 2 + y sup 2 >, s = < sin theta >
over theta,
t = < 1 - cos theta > over < theta sup 2 >
(when theta = 0, s = 1 and t = 1 / 2)

The spherical coordinates can be projec...