一种新的奇异研究方法及其应用实例

首先论证了奇异的运动学原理：物体上非共线三点的速度的三个法平面的交点，能落于该三点决定的平面上。这是物体上非共线三点的速度能确定此物体的螺旋运动的充分必要条件。依据此原理得到一种新的判别并联机器人机构奇异的简捷方法，且用此方法分析了3-RPS机构，首次得到此机构的三维奇异轨迹，并用线几何和力雅可比矩阵作了验算以证明方法的有效性。

A New Method of Singularity Research and its Example in Application

This paper firstly proves the kinematics principle of singularity, that the intersecting point of the three normal planes of the three velocities at the three non-collinear points in a rigid body lies in the plane determined by the three corresponding points. It is the sufficient and necessary condition that the velocities of three non-collinear points in a rigid body can determine a screw motion of the body. Based on this principle, we derived a simply and direct new method to distinguish the singularity of the parallel manipulator. With this new kinematics method to distinguish the singularity, the 3-RPS parallel manipulator is studied. Its singularity loci are obtained for some orientations for the first time and verified with Grassmann line geometry and the force Jacobian matrix.