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Determination of inertia tensor co-ordinates of manipulators on the basis of local matrices of homogeneous transformations

Szumiński P., Kapitaniak T.

Mechanics and Mechanical Engineering

2006

Vol. 10, nr 1

138-159

The aim of this paper is to present an algorithm for the determination of co-ordinates of inertia tensors of manipulator links and objects manipulated, which employs homogeneous transformations. A division of a manipulator link (an object manipulated) and local systems of reference, which correspond to this division, have been introduced. An introduction of additional local systems of reference allows for their most advantageous orientation in order to calculate the co-ordinates of inertia tensors of parts and elements, whose forms and shapes often cause serious problems during the calculation of inertia tensors with the traditional method. In order to transform geometrical dimensions of solid bodies and moments of inertia, an application of matrices of homogenous transformations, typical of the description of manipulator kinematics, has been suggested. Owing to the employment of homogenous transformations and their mappings, the proposed algorithm makes the determination of co-ordinates of inertia tensors much easier, especially in the case their shape is complex.