Multidual algebra and higher-order kinematics

Abstract

In this paper, using the vector and tensor calculus and the multidual algebra, a new computing method for studying the higher-order acceleration field properties in the case of the general rigid body motion is proposed. The results are coordinate-free and in a closed-form. Higher-order kinematics analysis of lower-pair serial chains with multidual algebra will be done. In particular cases, the properties for velocity, acceleration, jerk and jounce fields are given. This approach uses the morphism between the Lie group of the rigid displacements and the Lie group of the orthogonal multidual tensors.