Higher-Order Kinematics of Lower-Pair Chains With Hyper-Multidual Algebra

Abstract

Abstract This paper proposes a new computational method based on vector and tensor calculus and the properties of dual and multidual algebra for higher-order acceleration field in the case of rigid body motion. A closed-form coordinate-free solution is presented, this result being generated by the morphism between the Lie group of the rigid body displacements and the Lie group of the orthogonal hyper-multidual tensors. The solution is put into practice for higher-order kinematics analysis of lower-pair serial chains. Specific cases are chosen to evaluate the properties for velocity, acceleration, jerk, and jounce.