Mechanism Dynamics Sequence-Solution Method and Its Application 1 Preface

Preface Since the determination of the mechanism transmission principle, the key to mechanism design has been the selection of parameters, which is usually made through the rigid-body guidance method. Using the rigid-body method as guidance, first, according to clients' work requirements, several position points, and the angular displacements of links on the mechanism, are decided; then, through a series of calculations, mechanism parameters satisfying work requirements are obtained. Though this meets the kinematic requirements, however, the dynamics characteristics will not always meet the clients' desire for fast and efficient performance. So the dynamics analysis is very important in that it can provide a theoretical basis for the optimization of such mechanism dynamics. Various methods have been used for dynamics analysis of a rigid body, such as, the graphic method, Newton-Euler method, and energy method ͑Lagrange method͒. 1. The graphic method is complicated, low in efficiency, and liable to generate mistakes ͓1͔. 2. Newton-Euler method ͓2͔, including matrix method, vectorequation analytical method, basic-group method, and Kane method, generally requires for each link, six force and torque equilibrium equations in scalar form ͑for plane, three force-and-torque-equilibrium equations͒; or two force-andtorque-equilibrium equations in general-vector form, or one force-equilibrium equation expressed in dual vector, and then tens of linear algebra equations to be solved through the matrix method ͓3͔-to determine the constraint forces of all kinematic pairs, and the equilibrium force of the driving link ͓1,2,4-7͔. In Refs. ͓1,2,8͔, the vector-equation analytical method ͑in-step method͒ is used to find the applied force of a mechanism's kinematic pairs, by establishing first the applied force of the first kinematic pair, and then the applied force in the other ones. In Refs. ͓6,9,10͔, a basic grouping method on the basis of Assur Groups is proposed, in which the indivisible kinematic pair of a 0 degree of freedom ͑DOF͒, is taken as the basic unit of the mechanism, and for each unit the general subprograms suitable for corresponding kinetic analysis, and force analysis, are used. In the Kane equation ͓11͔ the vector-form driving force and inertial force are projected in some special directions, the concept of partial velocity and generalized force are adopted, and the vector multiplication cross substitutes for derivation, and thus values may be calculated through editing computer programs. In the Lagrange method, the dynamic equation is set up on the basis of the potential energy and kinetic energy of the system. In the matrix method, the vector equation analytical method, ͑in-step method͒, the basic-group method, the Kane method, and the Lagrange method, no consideration is made of the interference of the change in the direction of both the reverse-driving force, and the normal pressure of the friction force ͓1,2,4-7,3,8-13͔. In order to eliminate the above demerits, a dynamics sequence solution ͑DSS͒ is proposed. In establishing equations, the pin joint is taken as the movement center and all equations are solved sequentially. The results obtained from the preceding equation are used to decide the coefficient of the following one, so that the solution of the preceding equation makes known the unknown in the following equationand thus the equation is solvable. In addition, insertion of a condition-judgment statement during the solution process makes the calculation process self-adaptive to different work conditions