恒定雅可比3-PRRR移动并联机构及其传递性能研究  

3-PRRR Translational Parallel Mechanism with Constant Jacobian Matrix and Its Transfer Performance Analysis

作　　者：赵延治[1,2] 梁博文[1,2] 曹亚超[1,2] 赵铁石[1,2] 

机构地区：[1]燕山大学河北省并联机器人与机电系统重点实验室,秦皇岛066004 [2]燕山大学先进锻压成型技术与科学教育部重点实验室,秦皇岛066004

出　　处：《农业机械学报》2017年第1期333-338,367,共7页Transactions of the Chinese Society for Agricultural Machinery

基　　金：国家自然科学基金项目(51105322);河北省自然科学基金项目(E2014203176);河北省高等学校自然科学研究基金项目(QN2015040);中国博士后科学基金项目(2016M590212);燕山大学研究生创新项目(2017XJSS001)

摘　　要：提出了一种具有雅可比矩阵恒定特性的3-PRRR三维移动并联机构,当选取移动副作为主动输入时,该机构具有雅可比矩阵恒定的特性。基于螺旋理论分析了3-PRRR并联机构自由度,利用矢量法建立位置正/反解模型,进而得到了该机构的工作空间。基于传递力螺旋和主运动螺旋求解了该机构的雅可比矩阵,从得到的机构速度/力变化曲线可知,在确定的输入下,机构输出参数曲线在不同位姿下相重合,从而验证了该机构雅可比矩阵恒定。在此基础上,分析了该机构的传递性能,得到了分支传递功率与β(移动副和转动副轴线夹角)的关系曲线,可知输入功率不变时,机构的传递功率随着β的增大而减小。分别选取β为0°和30°时绘制该机构输出速度和力曲线,得到该机构在β为0°时传递性能最佳。A novel 3-PRRR three-dimensional translational parallel mechanism was proposed. Its Jacobian matrix was constant,when its prismatic pairs were chosen as the actuators. The degrees of freedom of the parallel mechanism was analyzed based on screw theory. The forward / inverse kinematic solution models were established to obtain its workspace by the vector method. Jacobian matrix of the mechanism was solved by the main twist screw and transmission wrench screw. Then,the curves of the output speed and force were drawn. According to the figures,the curves were completely coincident in different poses when the input parameters were certain. Thus,the conclusion that the Jacobian matrix of the 3-PRRR parallel mechanism kept constant was verified. On this basis, the transmissibility performance of the mechanism was further analyzed in order to obtain relationship between transmission power and angle β（ the angle between axis of the prismatic pair and its nearest pair-the revolute pair） of each limb. Finally,another important conclusion was got. It can be expressed as： when the input power was definite and invariant,the transmission power of the mechanism was decreased with the increase ofβ. Comparison was made between output speed and force curves in two cases that β were equal to 0° and30°,the transmissibility performance of the mechanism varied with β and the former was better than the latter. Similarly,after the transmissibility performances with other values of β were analyzed, the performance was optimal when β was 0°.

关 键 词：并联机构 螺旋理论 雅可比矩阵 传递性能 

分 类 号：TH112[机械工程—机械设计及理论]