Research On The Key Issues Of Mechanism Synthesis Based On Conformal Geometric Algebra

Mechanism synthesis is a critical issue in the robot mechanisms research,including type synthesis and kinematic synthesis.The pivotal part of them is the logical description of topological and dimensional characteristics of mechanisms,which can make the motion output characteristics be derived.Based on this,the mapping relation from mechanical per-formances to structural types and parameters can be established.The appropriate mathema-tical tool,which can provide a unified modeling and analysis method for structures and kinematics of mechanisms,is the key to this problem.Conformal geometric algebra（CGA）,which affords a concise and intuitionistic fra-mework of geometrical representation and computation,is selected as the main tool in this paper.The dervation of position and orientation characteristics for type synthesis and the generations of geometric trajectory and self-motion for dimensional synthesis are discussed,which are organized as follows.（1）Based on the 5-dimensional conformal space G^4,1,a line is described by six basis vectors according to the intersection of planes.The group of basis vector is used as the independent bases for the position and orientation characteristics of joint axes and motion output characteristics of links.A moving coordinates system,independent of positions of mechanisms,is built to express positions and orientations.The union of serial kinematic chains is defined by the outer product while the intersection of parallel kinematic chains is defined by the shuffle product,then the CGA-based description of position and orientation charcteristics of robot mechanisms is established.（2）The analysis procedure for parallel mechanisms（PMs）is introduced with the esta-blishment of the CGA-based method.Taking three mechanisms for instances,including3-RRCR,3-RPS and 4-5R PMs,the representation and derivation of position and orien-tation characteristics of joint axes,the motion output characteristics of limbs and moving platforms are revealed in detail.The rationality and effectiveness of the proposed method are validated,which is suitable for the automatic analysis of position and orientation cha-racteristics of general mechanisms.（3）The Peaucellier-Lipkin eight-bar linkage is discussed,and its kinematic model is built based on the represention of geometric entities using CGA.Different from the trade-tional elimination-based method,the displacement of the end-point is obtained by the geo-metric operation directly.Then the straight line trajectory of this linkage is proved.Based on the proposed CGA model,the dimensional relation of links is obtained,under the circu-mastances that the circular arc trajectory can be generated by this linkage.（4）According the intersection theory of surfaces,a novel mechanism that can gene-rate conics is established,based on two types of RPS kinematic chains that can generate the plane and cone.The position and orientation relation between the generated plane and cone can be changed by a revolute joint,so that the proposed mechanism can generate dif-ferent conics.Based on the description of the relation of geometric constraints using CGA,the analytic expression of the end-point and correspondent trajectoris are obtained.Two types of equivalent mechanisms are also proposed.（5）According to the motion output characteristics of self-motion mechanisms,the CGA models of a type of Stewart parallel platform and Griffis-Duffy platform are built based on the intersection theory of surfaces.The theory of cognate mechanisms is introdu-ced to realize the dimensional synthesis of double 3-SS mechanism,based on the analysis of the dimensional constraints.Furthermore,the dimensional characteristic of ratio is pro-posed and applied to constructing this type of self-motion mechanisms.