以设计结构紧凑、工作空间大的力/触觉反馈器为目标, 研究了Delta并联机构的运动学和工作空间特性。在改进Delta机构的基础上, 引入支链机构的偏置安装角度α, 利用矢量法求解了机构的位置逆解和正解, 并通过算例验证了方程求解正、逆解的正确性; 根据逆解公式推导出单开链子空间包络体边界方程, 绘制分析了驱动杆与摆动杆长短不同时3种情况下的子空间几何形状。然后,详细讨论了α对整体工作空间和机构总体外围尺寸的影响, 采用数值法得出了偏置安装角度α与工作空间最大内切球体体积的关系图、偏置角度与整体外围尺寸的关系图, 并利用matlab绘制出整体空间截面图。最后, 以上述最大内切球体为设计空间,结合雅克比矩阵条件数给出设计实例。验证结果表明, 采用该设计方法能够满足对Delta机构的优化设计要求。

To design a force/tactile feedback device with compact construct and a larger workspace, the kinematics analysis and working space algorithm were researched based on the Delta mechanism. Based on the improved Delta mechanism, a chain offset angle alpha was introduced. Positive and inverse kinematics were established by the vector method and their correctness were verified by taking a deduced equation as an example. According to the inverse kinematics formula, the envelope body equation of single-open-chain subspace was deduced and the geometric shape of the subspace was drawn under three situations while the length of drive rod is more than or equals to or less than that of oscillating rod. Then the influence of alpha on the whole workspace and mechanism size was deeply discussed. The relations between the offset angle and the volume of the maximum inscribed sphere, the offset angle and the whole mechanism size were derived using the numerical method. Moreover, the cross section view of the space was plotted by MATLAB. Finally, the maximum inscribed sphere was taken as the design space,and a design example was given by using the Jacobin matrix condition number. The results after verifying show that the designed mechanism meets requirements of optimized design Delta mechanisms.