A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

Yongquan Li,Yang Zhang,Lijie Zhang

doi:10.1186/s10033-020-00487-7

Yongquan Li, Yang Zhang + Show 1 more

Open Access

https://doi.org/10.1186/s10033-020-00487-7

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Abstract

The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

Highlights

Redundancy can be divided into actuated redundancy, kinematics redundancy and hybrid redundancy according to its characteristics
2 Introduction of Atlas Method In order to facilitate the analysis and type synthesis of parallel mechanisms, the degree of freedom (DOF) and constraints of mechanisms are visualized, i.e., the kinematics and constraints of mechanisms are represented by line graphs composed of straight lines and double arrow lines
Because this constraint and motion visualization combined with Grassmann line geometry theory makes it easier to study its dimension and lays a foundation for DOF analysis and type synthesis of parallel mechanisms

Summary

Introduction

Redundancy can be divided into actuated redundancy, kinematics redundancy and hybrid redundancy according to its characteristics. The redundant actuated is added to the P pair of PRPU branched chain, which can effectively eliminate the crawling defects of the intermediate slider. It can optimize and enhance the actuated carrying capacity on each branch of the parallel mechanism. Han et al [14] constructed a redundant actuated parallel mechanism by adding a PSS branch chain to the 3-PSS parallel mechanism, and the dynamics and control analysis are carried out. The constraint coupling of mechanism is accomplished within the branched chain unit, so that the redundant parallel mechanisms with non-over constraint and low-order over-constraint is obtained. The 4UPU redundant actuated parallel mechanism can be obtained by adding

The moving DOF

The second type PMs with closed loop unit

Conclusions

Branch chain assembly requirements