Kinematics simulation of serial manipulators

This paper presents a systematic development for finding position, velocity, and acceleration of one or more points of interest on one or more links of a serial manipulator. The system of equations given is well suited for direct kinematics and effectively supplies the influence coefficients or velocity Jacobians needed for a subsequent dynamics or kinetostatics simulation. An alternative to the Denavit-Hartenberg matri-ces is suggested, and a direct vector statics solution for actua-torforces and torques is provided. It is shown that all veloci-ties and accelerations (linear and angular) are simply expressed in terms of certain so-called star matrices. By exploiting the skew symmetry of these matrices as well as sparseness properties wherever possible, it is shown that the arithmetic operation counts can be reduced significantly in the calculations. The ideas presented here have been imple-mented in a computer program that was used to partially verify the practicality and efficiency of the techniques devel-oped. 1