CHAPTER 4
NEW APPROACH
Link-Frames Assignment
Some simplification in the mathematical description of the inverse kinematics problem can be obtained if certain simple rules for assigning the link-frames are applied.
In selecting frame Fi, the direction of vector zi is always chosen so that twist angle ai is in the interval [O,r). If ai = 0, then vectors zi_1 and zi are parallel and the common normal can be arbitrarily located along both axes. In this case the position of Frame Fi should be chosen so that di is equal to zero.
For an n-DOF robot, frame Fn, attached to the endeffector, can be chosen so that it differs from link frame Fn_1 only by a rotation of angle en about Zn_.l In other words, Fn can be selected so that dn = an = an = 0, without loss of generality. We prove this point for n = 6, but it is valid for any relevant value of n. Let us assume that Eq. (2.14) is to be solved with a 6-DOF manipulator for which d6, a6, or a6 is not equal to 0, then the homogeneous matrix transform A6 decomposes into
A6 = A6 B6
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