Method for the calculation of the combined motion time derivatives of optional order and solution for the inverse kinematic problems

The paper introduces a special method of transformation for joint representation of linear – e.g., rigid body – motions and their time derivatives. The product of the transformations, designated for the motion components of the resultant motion, provides the velocity, acceleration and the higher time derivatives up to optional order. There is a possibility to produce the analytic solution of the inverse problems and the constrained equation of the closed loop kinematic systems being at the limit value. The most simple types of approximate solutions may be obtained by truncating the algorithm.