Structural Synthesis And Analysis Of Translational Parallel Manipulators With Pa~2 Kinematic Joints

Parallel mechanism has drawn more and more attention due to its advantages of load carrying, high accuracy and more rigidity, etc, and become a hot topic around the world.However, the problem of structural synthesis of parallel robots is not settled properly. What is more, structural synthesis of lower parallel mechanism still is a hot topic in parallel robotics.Lower parallel mechanisms, especially those which can generate translations, still play an important role in the industrial. This thesis presents two translational parallel robots with Pa2 kinematic joints by resorting to displacement subgroups. Then, an analysis for the two robots are developed (including freedom analysis and kinematic analysis).A general kinematic joint Pa2, which can be considered as a generated mechanism from parallelogram, can not only provide a two degrees-of-freedom (DOF) translations. but also generate translations as passive joints. Comparing with passive translation joints, Pa2 kinematic pair has more advantages in generating stable translational motions. Besides, the mathematical model of Pa2 joints can be used to analyze those parallel mechanisms with this joint.The direct and inverse kinematic problems of 3-PPa2 are solved by resort to spatial closure vectors, and to obtain the solutions of both problems. The workspace of 3-PPa2,which is a result of intersecting three cylinders, is obtained by performing the closure equations. The velocity problem of 3-PPa2 is solved after obtaining the velocity equations,in which three types of Jaobians matrices are defined: direct Jacobian matrix, inverse Jacobian matrix and increase mobility Jacobian matrix.Also, the workspace of 3-PPa2 is investigate having a simple shape, which is the intersection of three cylinders, more accuracy to say, it is one cormer of the intersections.However, the volume of workspace enlarges with the increase of the dimensions of Pa2 joint.Three types of singular coifigurations of 3-PPa2 are investigated, na1ely direct singularity, inverse singularity and increase mobility singularity. In which, the inverse singularity is straightforward being the external boundary of workspace. However.,both direct singularity and increase mobility singularity are quite complex, which are difficult to indicate by using an singular surface. However, some singular configurations of 3-PPa2 are investigated, and their singular surface is obtained.Those parallel mechanisms with complicate closed chains are firstly analyzed in this thesis.lhich indicates the potential applications of Pa2 kinematic joints in structural synthesis of parallel robots, and also enrich the types of kinematic joints which can be used in the structural synthesis of parallel robots. The robot presented in this thesis,3-PPa2, has more compact structures and more simple kinematic solutions, in addition, it can enrich the family of lower parallel mechanisms, and make up robotic theory related to parallel mechanisms.