与传统工业串联机器人相比，后三个旋转关节轴线相交于一点、而前三个旋转关节轴线均不相交的六自由度串联机器人的工作空间较为完善，然而此类6R串联机器人逆解的求解较为复杂，限制了其应用。针对其逆解问题，提出一类新的Paden-Kahan子问题类型：将一点绕两个不相交且不平行的轴线依次旋转到指定点，以及其扩展问题类型：将一点绕两个不相交且不平行的轴线依次旋转直到该点到固定第一点和固定第二点的距离均为指定大小。通过构造与该点运动轨迹相垂直的垂直平面，推导和求解了该子问题的正解和逆解，结合其他已知的子问题，简化和求解此类6R串联机器人的逆解问题，并对其逆解的条件和数目进行讨论。与传统的消元法相比，采用该方法得到的逆解的几何意义更为明确、计算量少、求解效率更高，改进了此类6R串联机器人逆解算法。通过实例计算，验证了求解方法的有效性和可行性。
For an improved 6-DOR series robot of which the axes of the last three rotating joints intersect to one point and the axes of the first three rotating joints are non-intersect each other, its workspace is better than the workspaces of traditional industrial robots. But the inverse kinematics calculation for this improved 6-DOR series robot is complicate and cost large computing, which limit its application. In order to improve the performance of the algorithm for its inverse kinematics calculation, a novel Paden-Kahan sub-problem which can be described as letting a point rotate about two disjoint and non-parallel subsequent axes to the point appointed, and its extended problem which can be described as letting a point rotate about two disjoint and non-parallel subsequent axes to two points fixed with two distance appointed to each, are proposed and solved. By constructing a plane perpendicular to the motion trajectory of the rotating point, the forward and inverse kinematics problems of this novel Paden-Kahan sub-problem were solved. Combining with other known Paden-Kahan sub-problems, the inverse kinematics of the 6R series robots are simplified and solved. Then the constraint conditions and the situations of the number of its inverse kinematics solutions are discussed. With the method proposed, the geometrical significance signed for the inverse kinematics is clearer than that with traditional algebraic elimination method, and the operation efficiency of the inverse kinematics is improved. The effectiveness of the solving methods is verified through an instance with exact parameters.
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