Type Synthesis And Optimal Selection Of 1T2R And 2R1T Parallel Mechanisms Based On Conformal Geometric Algebra

Driven by the important requirements for high grade CNC machine tools and robots in the advanced equipment manufacturing industry,this thesis carries out the type synthesis,inverse kinematic analysis of all joints and type optimal selection of parallel mechanisms with one translational and two rotational motions(1T2R and 2R1T)by utilizing Conformal Geometric Algebra(CGA).The following contributions have been made.(1)Type synthesis.Based upon CGA,the type synthesis of 1T2 R and 2R1 T parallel mechanisms is implemented and unified in a general procedure.The finite motions of 1T2 R and 2R1 T parallel mechanisms are firstly described by CGA,and their intrinsic relations are explored.Then the available limbs are generated in a parametric and analytical manner and their axes layouts are determined.Finally,in order to prevent parallel mechanisms from having other DoFs except one translational and two rotational motions,the assembly conditions among available limbs are concluded to synthesize systematically 2R1 T and 1T2 R parallel mechanisms.(2)Inverse kinematics of all joints.Inverse kinematic analysis of parallel mechanisms is decomposed into several inverse kinematic problems of serial mechanisms.Based on the assembly conditions of all joints in each limb,the kinematic models of four kinds of basic limbs are established,and inverse kinematics of all joints in basic limbs are performed by the property of motor.Then the kinematic analysis of all joints in equivalent limbs is executed considering the function relationships between the motion variables in each equivalent joints' combination.Finally,with the help of the relationship between 1T2 R and 2R1 T parallel mechanisms,their kinematics of all joints are obtained.(3)Type optimal selection.The stiffness mapping model between all joints and the end-effector of parallel mechanisms is formulated by force analysis,stiffness analysis and virtual work principle.Then from the energy view of point,the topological evaluation indices are proposed,through the energy stored by the mechanism under the situation of unit deformation.Finally,the type optimization is carried out among seven kinds of 1T2 R parallel mechanisms,and the influences of the topology and arrangement of limbs on the stiffness of parallel mechanisms are discussed.