Dual tensors based solutions for rigid body motion parameterization

Rigid body displacement and motion parameterization is a research subject with continuous development in many theoretical and applied fields. A very important objective for the design of parameterization methods is to obtain a reduced number of algebraic equations and fewer variables for a more compact notation. This criterion increased the interest into tensorial based approaches for rigid motion parameterization. The present research analyzes the performance of tensorial parameterization and proposes new methods to compute the rigid-body motion parameters. Our rigid body motion parameterization solutions are developed using rigid bases of dual vectors, a new notion defined in this paper. Considering a rigid body motion, computational techniques are proposed for the orthogonal dual tensor, the screw parameters and the instantaneous screw parameters. The parameterization techniques proposed in this paper are described both algebraically and geometrically. Our solutions are sustained by the symbolic and numerical results gathered from Matlab implementations.