基于空间几何的无伴随运动并联机构分析与综合

Analysis and Type Synthesis of Parallel Mechanisms without Parasitic Motion based on Spatial Geometry

一移动两转动(1T2R)三自由度并联机构普遍存在的伴随运动对机构的运动精度及性能有不利影响,为得到一系列1T2R无伴随运动的并联机构,利用空间几何理论及螺旋理论对无伴随运动并联机构进行分析与综合。基于空间几何理论分析了无伴随运动并联机构的转轴条件,结合螺旋理论分析了该类机构动平台平面与约束螺旋的空间位置关系,将至少拥有1T2R自由度的支链分成4类,分析[R]-型支链在不同支链布局下的约束螺旋位置及转轴位置对伴随运动的影响,从而给出了1T2R无伴随运动并联机构的构型准则及结构条件,并通过构型综合得到了105种无伴随运动并联机构。对一种新型2RPU-RPRU无伴随运动并联机构进行了运动学分析,验证了该方法的正确性。

Parasitic motion widely exists in general 1 T2 R(one translation and two rotations) parallel mechanism, which has a negative influence on motion accuracy and performances of mechanism. To obtain a series of 1 T2 R parallel mechanisms without parasitic motion, the analysis and type synthesis of parallel mechanisms are conducted based on spatial geometry and screw theory. The condition of rotational axes of parallel mechanism without parasitic motion is analyzed based on spatial geometry theory, then the spatial position relationship between the plane of moving platform and constraint wrenches is explored with screw theory. Branch chains with at least 1 T2 R degrees of freedom are divided into four types, and positions of constraint wrenches and rotational axes which cause parasitic motions directly are discussed with different [R]-branch chain layouts. The synthesis criteria and geometrical conditions of 1 T2 R parallel mechanism without parasitic motion are deduced, and 105 kinds of mechanism without parasitic motion are obtained through type synthesis. The kinematics of a new 2 RPU-RPRU parallel mechanism without parasitic motion is analyzed to verify the correctness of the method.