多体系统中邻接体相对运动显式约束方程的普遍形式OA

The key to recursive kinematics of a multibody system is to study the relative motion between two adjacent bodies constrained by a joint.In this work,vectors and finite rotation tensors are used to describe the translation and rotation of rigid bodies with general spatial motion,respectively.Starting from the basic kinematics of rigid bodies and through rigorous deduction,the theorem of explicit joint constraint equation(EJCE)is proposed:the difference between the spatial acceleration twists of the outboard and inboard joint coordinate systems is a linear function of the second-order time derivatives of the joint coordinates,where the Jacobian matrix is a function of time and joint coordinates,and the inhomogeneous bias term is a function of time,joint coordinates and their first-order time derivatives.This theorem does not rely on the specific types of joints,and is independent of the choice of joint coordinate systems as well as joint coordinates,and is thus universal.Further,a calculation method for the Jacobian matrix in the EJCE is presented,which does not depend on the specific type of a joint and the selection of rotation parameters of the joint coordinates.In a final example,a spherical joint that constrains two adjacent bodies is illustrated.The Jacobian matrix in the EJCE is obtained using both the proposed method and the Euler's kinematic equations.The results are consistent,which validates the proposed method.This paper clarifies the existence of the general form of the EJCE and the computability of its Jacobian matrix,which is of theoretical significance for the recursive kinematics of multibody systems.