基于加权广义逆求解被动过约束刚-柔耦合并联机构的受力问题  

Solving the Force Problem of Passive Overconstrained Rigid-flexible Mixed Parallel Mechanisms Based on the Generalized Inverse of Weighted Moore-Penrose

作　　者：刘文兰[1] 许允斗[1,2] 陈亮亮[1] 姚建涛[1,2] 赵永生[1,2] 

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

出　　处：《机械工程学报》2016年第23期84-93,共10页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51275439);国家重点基础研究发展计划(973计划;2013CB733000);燕山大学青年教师自主研究计划课题(13LGA001)资助项目

摘　　要：提出一种直接应用力映射矩阵的加权广义逆求解一般被动过约束并联机构(指分支提供给动平台的约束力/力偶数目大于等于1的被动过约束并联机构)的超静定受力问题的方法。基于小变形叠加原理和螺旋理论得到了分支约束力螺旋系刚度矩阵的一般表达式。推导一般被动过约束并联机构的各分支约束力螺旋系幅值与六维外力之间的映射关系式,进而证明了该关系式恰好是力映射矩阵的加权广义逆,其中加权矩阵为各分支约束力螺旋系刚度矩阵组成的分块对角阵的逆。以3-RRC空间三自由度被动过约束并联机构和一个并联振动平台为例,直接应用加权广义逆求解了机构各分支约束力螺旋系的幅值,并进行仿真验证。基于加权广义逆求解被动过约束并联机构的超静定受力问题大大简化了求解过程且解的形式统一、简单。A method to solve the statically indeterminate force problem of the general passive overconstrained parallel mechanisms（PMs） is proposed by using the generalized inverse of weighted Moore-Penrose of the force mapping matrix. The general passive overconstrained PMs refer to the PMs in which each limb supplies one or more constraint forces/couples（including driving forces/torques） to the moving platform. The general expression for the stiffness matrix of the limb＇s constraint wrenches is derived based on the superposition principle of micro-deformation and screw theory. The mapping relationship between the magnitudes of all limbs＇ constraint wrenches and the external wrench is obtained, which just is the generalized inverse of weighted Moore-Penrose of the force mapping matrix. The weighted factor matrix is the inverse matrix of a block diagonal matrix composed of the stiffness matrices of each limb＇s constraint wrenches. Taking 3-RRC overconstrained PM and a parallel vibration platform as examples, the magnitudes of all limbs＇ constraint wrenches are solved through the generalized inverse of weighted Moore-Penrose of the force mapping matrix. The correctness of the method is verified by the simulation work. The solving process of the statically indeterminate force problem of passive overconstrained PMs is greatly simplified, and the solution is obtained with a unified and simple form by using the generalized inverse of weighted Moore-Penrose.

关 键 词：加权广义逆 被动过约束并联机构 超静定 受力分析 约束力螺旋系刚度矩阵 

分 类 号：TH112[机械工程—机械设计及理论]