Singularity Analysis of Planar Cable-driven Parallel Mechanisms with Grassmann Geometry

Abstract

Cable-driven parallel mechanism is singular when some wrenches acting on the cables are deficient.Based on the definition,the cables are defined as line vectors.The linear correlation among cables is analyzed with Grassmann line geometry,and the singularity of the mechanism could be easily testified.The geometry condition of singular free planar mechanism is presented.The singularities of some mechanisms are analyzed by the line geometry method,and the singular free mechanisms are designed based on the geometry condition.According to the geometry condition,the singular mechanisms are improved through changing the dimensions or add some cables to avoid the singularity.At last,the numerical method with Jacobian matrix is used to analyze the singularity,and the result demonstrates that the improved mechanisms avoid the singularity which original mechanisms have.The result also shows that Grassmann line geometry is applicable to the analysis of cable-driven parallel mechanisms.