On the Global Optimum Disk Counterweight Balancing of an Eight-Bar Linkage

摘要

It is the main concern, to investigate the designs of installing disk counterweights on moving links with fixed revolute joints of a type of eight-bar linkages, to minimize (1) the shaking force only with no size limitations on the counterweights, (2) the sum of its root-mean-squared (rms) shaking force, shaking moment and driving torque without counterweight size constraints, and (3) the sum of its rms shaking force, shaking moment and driving torque with counterweight size constraints, whose counterweight contours need be tangential to the fixed pivot centres. Applying the proposed inertial parametrization, the models for the kinematic and kinetostatic analyses are developed. Based on them, the models of the optimum balancing designs of the above problems are proposed. Additionally, for each problem, the necessary and sufficient conditions of the optimal solution are also derived; the necessary conditions are then applied to find all optimum candidates, and then the sufficient condition is used to check which of these candidates are the local optimums; consequently, the global optimum can be found among them. An example for each problem is included, to demonstrate the usage of the proposed models and to show the balancing effects of the optimum designs. According to the result of each problem, only one solution satisfies both of the necessary and sufficient conditions, which is also the same as that searched by using the proposed optimal balancing design model. Thus, the proposed models can be applied to locate the global optimums of the balancing design problems, respectively.