The properties of matrix operations and the properties of Hartenberg-Denavit's co-ordinate system's transformation matrices were used for deriving a dependence facilitating an easier determination of the links' angular velocity vectors in the link-related co-ordination systems. The use of derived dependence does not require determining products of transformation matrices nor inverse matrices. The numbers of necessary algebraic operations for previous and simplified dependences was set up. The use of a simplified dependence was illustrated by a numerical example.

The paper presents the algorithms for kinematic analysis, trajectory planning, dynamics of kinematic chain and driving units elaborated for manipulators and robots with kinematic chains of serial structure with revolute pairs with perpendicular or parallel axes. Elastic deflections of driving units as well as action of external forces on end-effector have been taken into account. The simulating software was created using the modular structure of modeling process. The application of software for testing the robots accuracy and running speed acc. to ISO 9283 is also presented.