Simultaneous Minimization of Shaking Moment , Driving Torque , and Bearing Reactions of Complete Force Balanced Linkages

The present paper deals with an integrated design approach for complete force balanced planar linkages. It combines kinematic synthesis, dynamic balancing design, and the design of speed trajectory of input link in the same design step, satisfies kinematic design requirements, and reaches the trade-off of dynamic balancing with complete force balancing. By properly designing the variable input speed trajectory, the balancing parameters of moving links and link dimensions of the given or desired mechanisms, the expected output motion characteristics, and dynamic balancing performance are obtained. The input motion characteristics are designed with Bezier curves. Optimization is applied to find optimal design parameters for meeting kinematic and dynamic design requirements and constraints. The examples are given to demonstrate the feasibility of the proposed method. INTRODUCTION Linkages are widely used in mechanical devices owing to their simplicity of structure, ease manufacturing, high reliability, and low cost. Kinematic synthesis and dynamic design are both essential steps in the development of mechanisms and are usually treated as separate stages in the design process. Traditionally, the input speed of the driving link is assumed constant. The problem of vibration, noise and fatigue comes mainly from shaking force of the mechanisms, especially in high-speed applications. Therefore, the complete force balancing is normally an expected goal to the designers. Unfortunately, it usually conflicts with other dynamic performance such as shaking moments, bearing reaction forces, and driving torque of the mechanisms. Since, the dynamic balancing performance of mechanisms mentioned above is mainly affected by their inertial properties and kinematic characteristics of the gravities of each moving link. Furthermore, they are dominated by the characteristics of the input link and link dimensions. Therefore, our purpose here is to develop a novel design method that integrates kinematic synthesis, dynamic balancing design, and input speed trajectory design to reach the trade-off of dynamic balancing and satisfy the kinematic requirements and constraints as well for force balanced four-bar linkages by varying the speed of the input link, counterweighing on moving links, and synthesizing the dimensions of each link. Relatively little research has been devoted to the techniques for combining kinematic synthesis and dynamic design. Starr (1973) considered the problem of determining the constrained path of a mechanism member between specified positions such that some quality of dynamic performance is optimized. Conte et al. (1975) synthesized the crank-rocker path generating mechanisms with prescribed timing by optimization based on minimizing shaking force, shaking moment, driving torque, and bearing reactions, respectively. Yan and Soong (2001, 2002, 2004) presented a kinematic synthesis and dynamic balancing integrated design approach for four-bar linkages. * Associate Professor, Department of Automation Engineering, Kao Yuan University, Kaohsiung 82141, TAIWAIN, R.O. C. Variable input speed mechanisms were seldom discussed in the literature. Tesar and Matthew (1976) derived the motion equation of the follower by considering the case of variable speed cams. Yan ** Professor, Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, TAIWAIN, R.O. C.