| The parallel mechanism(PM) has the characteristics of high rigidity, compact structure, quick action, no accumulation of errors comparing with the series mechanism, so they have great superiority in industry application. PMs have attracted more and more attentions since the year of 1970 especially the PMs with 3 degrees of freedom (DoF) and 6 DoF, the researches about the 4 and 5 DoF PMs are relatively less than the above-mentioned two types of PMs for their complexity in structure and difficulties in kinematics analysis, While the 5 DoF PMs as mentioned in this paper with the 3 translations and 2 revolutions (3T2R) have important role in applications that require positioning and orienting a body in space. The lack of researches about T3R2-type PMs will result to the drawbacks and the limitations of the industry application.The motion performance analysis have the direct relationship with the Control Strategy in practical application, and it often refers to the forward kinematics analysis, Jakobian matrix analysis, static formulation establishment as well as the acceleration formulation establishment. Besides, the PMs' workspace as well as the singularity loci Analysis is needed to gets a better understanding under the working condition. The reachable workspace of the PM is defined as all the positions that can be reached by the central point of the platform, it represent the working range of the end effecter. The singularity means that the Jacobian matrix determinant of the PM equals zero, in this condition, the end effecter will lose or increase it's DoF and the driving forces of the manipulator will not balance the generalized forces at the same time. The PMs with fully-isotropic structure will be free from the influence of undesirable phenomena mentioned above. The fully-isotropic PMs with decoupled motions will have a one-to-one correspondence between the actuated joint velocity space and the external velocity space of the moving platform, and it will be free from the singularity as well. So, the kinematics of the PM will be imported and the controlling strategy will be simplified. Under the foregoing content, the paper firstly used the 5SPS+1UPU PM as the example to analyze its motion performance. The S denotes the spherical joint, the U denotes the universal joint, and the P denotes the prismatic joint, the 5SPS denotes the 5 actuate chains, 1UPU denotes the 1 constraint chain. The vector approach and screw theory are used in the kinematics analysis. The vector approach for forward kinematics solution will be intuitive and simple, and all the possible solutions will be obtained according to the formulation and input parameter. The Jacobian matrix can be derived through the screw theory easily, and then the velocity formulation can be established. Although the Jacobian reflect the singularity of the PM, the singularity loci can be known as well by analysis the matrix using research on screw system dependency under different space geometrical conditions. The acceleration formulation of the PM will be obtained though the differentiation at the both sides of the velocity formulation. Secondly, analytic and calculation methods are used in the analysis of the workspace and singularity, the several possible forms as well as its singularity loci in workspace is derived. Lastly, to improve the performance of the 3T2R type PMs, the fully-isotropic structure synthesis is made using screw theory, a serial of the structure forms of this type PMs are proposed at the end. |
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