3自由度柔索并联机构的运动轨迹规划

Motion Trajectory Planning of 3-DOF Cable-driven Parallel Mechanism

首先基于3自由度柔索并联机构模型,通过对索端重物进行正、逆运动学分析找到重物位置坐标与索长输入的相互关系。在此基础上,运用达朗贝尔原理推导出各柔索索端拉力与重物位置及柔索长度之间的关系。此过程中建立的非齐次线性方程组,证明了其具有无穷多组解,并采用广义逆矩阵的相关理论求解获得该方程组的最小范数解,即任意一时刻索端拉力的最优解;然后,在满足约束条件的前提下,寻找该并联机构的工作空间,即重物运动轨迹的范围。最后,对重物实现空间螺旋线轨迹进行了仿真,结果表明该机构能使重物的运动满足轨迹要求并具有较好的平稳性。仿真结果也为后续的对实现重物按规划轨迹运动的机构控制提供了理论基础。

Based on the 3 - DOF cable-driven parallel mechanism, firstly, the relationship between the load position and the cable length was derived by using the kinematics together with the inverse kinematics analysis. Secondly, in order to find out the end forces of every cable under a certain cable length and load position, the dynamic analysis was carried out based on the D＇Alembert＇s principle. Results showed that the established dynamical equations were a group of nonhomogeneous linear equations, which were proved to have a great deal of solutions, here the theory of generalized inverse matrix was introduced to obtain the optimization solution, which was called the minimum norm solution of the end forces. And then, several restricted conditions were put forward to do the workspace drawing of the mechanism, thus the motion area of the load was restricted. Finally, simulation of the load moving along a spatial helical shaped trajectory was demonstrated, which indicated that the 3-DOF cable - driven parallel mechanism was able to actualize a smooth motion of the load. Besides, the simulation results also offered some theories for the future control of the mechanism under a planning trajectory.