多能域过约束并联机器人系统动力学建模方法

Dynamic Modeling Method for Overconstrained Multi-energy Domain Parallel Manipulator

采用旋量键合图建立球面2-DOF过约束并联机器人机电两种能量并存系统动力学模型,该方法相对传统力学原理动力学建模方法的优点是建模过程规则化,能够得到适合于现代控制理论的空间并联机构状态方程。所建动力学模型只有36个方程,但由于被动过约束(公共约束和冗余约束)和主动过约束(冗余驱动)的存在,共有43个未知量需要求解。为此,针对被动过约束问题,分析三个分支变形引起末端相对于球心O的位移量,增加了6个变形协调补充方程;针对主动过约束问题,提出了采用输入力优化的方法,增加了1个补充方程,最终得到了该机器人完整的多能域系统动力学全解模型。通过数值算例,验证了该方法的可行性和合理性。该方法可以推广到其他包含机、电、液、气的多能域过约束并联机器人系统,为该类多能域机器人系统动力学建模分析提供了一种新的思路。

The dynamic model of the spherical 2-DOF overconstrained parallel manipulator which contains electrical and mechanical subsystem is established by using the screw bond graph. It can obtain the state equations of space parallel mechanism which suitable for control systems. Because of the existence of the passive overconstrained （common constraints or redundant constraints） and active overconstrained （actuation redundancy）. There are 43 unknown variables need to be solved, but only 36 equations in the dynamic model. Therefore, in order to solve the problem of passive overconstrained, the displacement of the chains, end which is caused by chains deformation relative to the center of sphere O is analyzed, respectively. And six supplementary equations of deformation compatibility are added. Aiming at the issue of active overconstrained, the method of driving force optimization is proposed, so the last one supplementary equation is added. Finally, the complete dynamic model of the parallel manipulator is obtained. And then the feasibility and rationality of the method are verified by numerical examples and verification. It also makes a foundation for the following research on the dynamic parameter identification of the parallel manipulator.