并联机构的螺旋理论坐标简化方法

摘要

螺旋理论求解并联机构时,运动螺旋通常采用6个坐标表示.但是,对于某些并联机构,其所有的运动螺旋存在相同的恒为零的坐标.求解这些特殊的并联机构时,可将这些恒为零的坐标去掉,对坐标进行简化.用简化后的坐标表示运动螺旋求解并联机构,相当于对问题进行了降维处理,从而简化了求解过程.转动副的特殊轴线方向以及移动副的特殊移动方向会使得表示它们的运动螺旋中某些坐标恒为零,根据运动螺旋中恒为零的坐标数以及恒为零的坐标次序不同,对运动副进行分类.对这些运动副进行组合,构成单开链,进而综合出所有的可简化成3个坐标表示的三自由度并联机构,给出了这些机构的运动螺旋的简化坐标及反螺旋计算公式,并给出了部分机构的简图.采用简化后的坐标求解这些并联机构,可有效地简化分析过程,降低求解难度.%When solving the parallel mechanisms based on screw theory,the kinematic screws are usually expressed with six coordinates.However,for some parallel mechanisms,all the kinematic screws have the same constant zero coordinates.When solving these special parallel mechanisms,the same constant zero coordinates can be removed to reduce the coordinates.Using the reduced coordinates expressing kinematic joints to solve the parallel mechanisms is equivalent to lowering the dimensions of the problem,thus simplifying the solving procedure.The special axis configuration of revolute joints and the special moving direction of prismatic joints can make some coordinates of the kinematic screws,which denote these kinematic joints be constant zero.The kinematic joints are categorized based on different counts and order of constant zero coordinates of the kinematic screws.Single open chains are formed by these types of kinematic joints and then all 3-DOF parallel mechanisms which can be reduced to three coordinates are synthesized.The reduced coordinates which denotes the kinematic screws of the parallel mechanisms and the formula of reciprocal screws based on the reduced coordinates are presented.Some sketches of the parallel mechanisms are also proposed.Solving these parallel mechanisms based on the reduced coordinates can efficiently simplify the analyzing procedure and decrease the difficulty of solving.