Mechanism and Machine Theory vol:31 issue:2 pages:135-148
This paper symbolically calculates the derivatives of a serial kinematic chain's velocity mapping. The derivatives are taken with respect to a change in one of the joint angles, as well as with respect to time. The result is a linear mapping, whose explicit form depends on the mathematical representation chosen for the Cartesian twist of the end effector. Three of the most common representations are treated: the ''inertial'', ''body-fixed'' and ''hybrid'' representations. Numerical calculations illustrate the correctness of the presented results.