基于并行计算的杆长和惯性参数可变的平面闭链机构动力学解析模型

Analytical Dynamic Model for Planar Close-chain Linkages with Alterable Length and Inertia Parameters Based on Parallel Calculation

基于凯恩动力学方程和数字-符号方法,提出基于构件子模型和并行计算建立杆长和惯性参数可变的平面闭链机构动力学解析模型的方法,并对驱动构件杆长和质量变化对驱动力/力矩的影响进行研究。采用封闭矢量法对平面闭链机构进行运动分析,得到各构件的速度和加速度表达式;将独立广义坐标以及杆长和惯性参数作为符号量,其余参数处理为数字量,离线生成各动力学子模型矩阵元素的实时代码,然后由叠加得到机构总的驱动力/力矩。针对各构件的子动力学模型,提出一种基于子模型动力学并行算法的实时代码优化方法。由于动力学模型的离线建立和优化以及采用并行计算结构,简化了机构的动力学模型,大大减少了在线计算时间,从而为机构的实时控制提供了有利条件。给出的动力学仿真实例证明了此方法的有效性。

Analytical dynamic model based on the sub model of links and a parallel algorithm for planar close-chain mechanisms, in which lengths and inertia parameters of links can be changed, is established based on Kane dynamic equation and numeric-symbolic approach. The influence of lengths and mass of driving links on driving force / torque are also studied. The close vector is applied in the kinematical analysis of planar close-chain mechanisms and expressions of velocity and acceleration of links are derived. Real-time code of matrix elements of each sub model, in which lengths and inertia parameters of links as well as generalized coordinates are expressed as symbols, the other variables as numeral, are derived off-line. Then the total driving force / torque of planar close-chain mechanisms are obtained by piled add. An optimization method of real-time code based on the parallel algorithm of sub model of links is proposed. The procedures of dynamic modeling and real -time code optimization can be performed off-line, and parallel calculation structure is adopted, therefore on-line calculation time can be reduced greatly, which is of advantage to real-time control of mechanisms. The examples of dynamic simulation are given for illustration.