Type synthesis of 1T2R and 2R1T parallel mechanisms employing conformal geometric algebra

2017 ◽

Author(s):

Ying Zhang ◽

Qizheng Liao ◽

Shimin Wei ◽

Duanling Li

Keyword(s):

Geometric Algebra ◽

Solution Process ◽

Kinematic Chain ◽

Polynomial Equation ◽

Solution Procedure ◽

Conformal Geometric Algebra ◽

Forward Kinematics ◽

Parallel Mechanisms ◽

Mathematics Mechanization ◽

Rotational Angle

In this paper, we propose a novel solution process for the forward kinematics of general 3-RPS parallel mechanisms based on conformal geometric algebra (CGA). First of all, the position of one of the three spherical joints is expressed in the rotational angle about the axis of one kinematic chain RPS. Secondly, the other two spherical joints can be determined by this angle via CGA operation. Thirdly, an explicit 16th-degree univariate polynomial equation is reduced from two geometric constraint equations. At last, one numerical example is employed to verify the solution procedure. The novelties of this paper lie in that (1) the modeling formulation and the elimination procedure have intrinsic geometric intuition due to the use of CGA and (2) the 16th-degree polynomial equation without extraneous roots is explicitly formulated and suitable for implementing the mathematics mechanization of this problem.

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Structural Analysis of Parallel Mechanisms Using Conformal Geometric Algebra

Intelligent Robotics and Applications - Lecture Notes in Computer Science ◽

10.1007/978-3-319-43506-0_14 ◽

2016 ◽

pp. 162-174

Author(s):

Lubin Hang ◽

Chengwei Shen ◽

Tingli Yang

Keyword(s):

Structural Analysis ◽

Geometric Algebra ◽

Conformal Geometric Algebra ◽

Parallel Mechanisms

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POC Analysis of Parallel Mechanisms Based on Conformal Geometric Algebra Description Method

Lecture Notes in Electrical Engineering - Mechanism and Machine Science ◽

10.1007/978-981-10-2875-5_31 ◽

2016 ◽

pp. 367-378 ◽

Cited By ~ 1

Author(s):

Chengwei Shen ◽

Lubin Hang

Keyword(s):

Geometric Algebra ◽

Conformal Geometric Algebra ◽

Parallel Mechanisms

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Finite Motion Analysis of Parallel Mechanisms with Parasitic Motions Based on Conformal Geometric Algebra

Advances in Applied Clifford Algebras ◽

10.1007/s00006-018-0832-4 ◽

2018 ◽

Vol 28 (1) ◽

Cited By ~ 2

Author(s):

Xinming Huo ◽

Yimin Song

Keyword(s):

Motion Analysis ◽

Geometric Algebra ◽

Conformal Geometric Algebra ◽

Parallel Mechanisms ◽

Finite Motion

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Type Synthesis of 1T2R Parallel Mechanisms Using Structure Coupling-Reducing Method

Chinese Journal of Mechanical Engineering ◽

10.1186/s10033-019-0403-1 ◽

2019 ◽

Vol 32 (1) ◽

Author(s):

Haitao Liu ◽

Ke Xu ◽

Huiping Shen ◽

Xianlei Shan ◽

Tingli Yang

Keyword(s):

Explicit Form ◽

Parallel Mechanism ◽

Analytic Solutions ◽

Forward Kinematics ◽

Parallel Mechanisms ◽

Type Synthesis ◽

Real Time Control ◽

Time Control ◽

Topological Characteristics ◽

Zero Coupling

Abstract Direct kinematics with analytic solutions is critical to the real-time control of parallel mechanisms. Therefore, the type synthesis of a mechanism having explicit form of forward kinematics has become a topic of interest. Based on this purpose, this paper deals with the type synthesis of 1T2R parallel mechanisms by investigating the topological structure coupling-reducing of the 3UPS&UP parallel mechanism. With the aid of the theory of mechanism topology, the analysis of the topological characteristics of the 3UPS&UP parallel mechanism is presented, which shows that there are highly coupled motions and constraints amongst the limbs of the mechanism. Three methods for structure coupling-reducing of the 3UPS&UP parallel mechanism are proposed, resulting in eight new types of 1T2R parallel mechanisms with one or zero coupling degree. One obtained parallel mechanism is taken as an example to demonstrate that a mechanism with zero coupling degree has an explicit form for forward kinematics. The process of type synthesis is in the order of permutation and combination; therefore, there are no omissions. This method is also applicable to other configurations, and novel topological structures having simple forward kinematics can be obtained from an original mechanism via this method.

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

Chinese Journal of Mechanical Engineering ◽

10.1186/s10033-020-00487-7 ◽

2020 ◽

Vol 33 (1) ◽

Author(s):

Yongquan Li ◽

Yang Zhang ◽

Lijie Zhang

Keyword(s):

Closed Loop ◽

Screw Theory ◽

Line Graph ◽

Degree Of Freedom ◽

Parallel Mechanisms ◽

Type Synthesis ◽

Allocation Criteria ◽

Grassmann Line Geometry ◽

Moving Platform ◽

Atlas Method

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.

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