H形并联机构运动学分析与样机精插补控制实验

Kinematic Analysis and Experiment of H-shaped Parallel Mechanism

对一种两自由度的H形并联机构进行了运动学分析,求出了其机构自由度,运用运动学叠加原理求出了其位置正解和逆解,利用Jacobian矩阵的条件数对其进行了运动性能评价,分析了其可达工作空间。计算结果表明该机构Jacobian矩阵的条件数恒等于1,具有优越的各向同性性能和广阔的可达工作空间。通过齐次坐标变换和矩阵分解对其位置逆解模型进行了进一步分析,得出该机构输入坐标与输出坐标轨迹具有几何相似的特点,并推导了输入与输出之间合速度及合加速度的关系,据此提出了使用通用的插补控制器对其进行精插补控制的方法,而不必开发专用的插补控制器。制作了该机构的样机,对其进行了精确定位、直线/圆弧插补、连续插补等实验,实验结果证明了所建模型的正确性。

Through kinematic analysis of the H-shaped parallel mechanism, the degree of freedom was derived. The inverse and forward position model of this mechanism were established by employing kinematic superposition principle and the analytical solution was obtained. The condition number of Jacobian matrix was derived and the workspaee was analysed. The result of the calculation shows that this mechanism had perfect isotropic properties and specious workspace. Further analysis of the inverse position solution adopting homogeneous transformation and matrix decomposition indicated that the trajectory between the input and output coordinate was geometrically similar. Based on that, a control strategy for fine interpolation only using general motion controller was proposed. A model machine was developed and a series of experiments were carried out, such as line/circle interpolation, continuous interpolation and etc. The results suggest that the mathematical model established for this parallel mechanism was correct.