Direct Kinematics of Planar Parallel Mechanisms Based on Conformal Geometric Algebra

doi:10.7652/xjtuxb201803011

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Direct Kinematics of Planar Parallel Mechanisms Based on Conformal Geometric Algebra

更新时间：2025-07-09

- Direct Kinematics of Planar Parallel Mechanisms Based on Conformal Geometric Algebra
- Vol. 52, Issue 3, Pages: 76-82+90(2018)
- 作者机构：
  
  北方工业大学机械与材料工程学院,北京,100144
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201803011
  CLC： TH112
- Online First：10 March 2018，
  
  Published：2018
- 稿件说明：
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Direct Kinematics of Planar Parallel Mechanisms Based on Conformal Geometric Algebra[J]. 2018, 52(3): 76-82+90.
DOI：

Direct Kinematics of Planar Parallel Mechanisms Based on Conformal Geometric Algebra[J]. 2018, 52(3): 76-82+90. DOI： 10.7652/xjtuxb201803011.

摘要

提出了一种基于共形几何代数(CGA)求解所有1 140种由转动副和移动副任意组合而成的平面并联机构的位置正解解析法。应用组合数学理论阐明了由转动副和移动副组成的平面并联机构共有1 140种类型; 根据各支链的长度约束条件

建立了涵盖1 140种平面并联机构类型的等效机构模型; 应用共形几何代数框架下的刚体平移和旋转运动表示

建立了等效机构模型的位置正解数学模型

只需通过简单的线性消元

即可推导出该位置正解问题的符号形式一元六次输入输出方程

从而可快速获得该问题的全部解析解

无增根也无漏根。基于计算机代数计算系统Maple16进行编程

通过2个数字实例验证了方法的正确性和有效性。

Abstract

A novel algorithm is proposed to solve the direct kinematics problem of arbitrary planar three-legged parallel mechanism composed of revolute joints R and prismatic joints P based on conformal geometric algebra(CGA). It is proved that there exist 1 140 possible forms of planar three-legged parallel mechanisms composed of revolute joints R and prismatic joints P by using combinatorics

and the equivalent mechanism model covering all these 1 140 forms is presented in terms of the constraints of each leg length. The mathematical model of the equivalent mechanism is built by using the expressions of rotation and translation under the CGA framework. Using the simple linear elimination

the symbolic input-output equation with 6th degree can be deduced from the mathematical model and all solutions can be obtained. Two numerical examples are given to demonstrate the efficiency of the algorithm based on Maple16. The results show that this algorithm can simplify the computation and is suitable for computer programming.

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references

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