基于共形几何代数的Stephenson-Ⅲ型机构的死点辨识

邱健; 范守文

基于共形几何代数的Stephenson-Ⅲ型机构的死点辨识

邱健,
范守文

1.
电子科技大学机械电子工程学院, 成都 611731

基金项目:

国家自然科学基金项目(51175067)

机械传动国家重点实验室开放基金项目(SKLMT-KFKT-201010)

流体动力与机电系统国家重点实验室开放基金项目(GZKF-201029)资助

详细信息

作者简介:
邱健(1986-)，硕士研究生，研究方向为机械产品设计缺陷辨识，qiujian987@163.com;范守文(联系人)，教授，博士生导师，shouwenfan@263.net

邱健(1986-)，硕士研究生，研究方向为机械产品设计缺陷辨识，qiujian987@163.com;范守文(联系人)，教授，博士生导师，shouwenfan@263.net

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出版历程
- 收稿日期: 2010-10-06
- 刊出日期: 2015-06-10

Identification of Dead-center Positions for Stephenson-Ⅲ Linkage Mechanisms Based on the Conformal Geometric Algebra

1.
School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu 611731

摘要

摘要: 基于共形几何代数方法建立了Stephenson-Ⅲ型机构的闭环约束方程,运用欧拉公式将方程表示成复数指数形式,描述了公式中各参数与共形空间中各矢量的相互关系,推导出了求解连杆机构运动姿态的输入-输出方程组,并在给定输入下得到了机构位置解。根据各输入杆变量的Jacobian矩阵的行列式的值等于0,推导得出了机构死点位置的判别式,得到了在死点构型下机构的位置解,通过与传统数值法计算结果的比对,验证了该方法的正确性和有效性。
- Stephenson-Ⅲ型机构 /
- 死点 /
- 共形几何代数 /
- 雅可比矩阵
Abstract: Closed-loop constraint equations of Stephenson-Ⅲ linkage mechanisms are established based on the Con-formal Geometric Algebra (CGA), by using Euler formula.The closed-loop equations are expressed as compound exponential form. Mutual relationships between various parameters in the formula and vectors in con formal space are described.Depending on given input, input-output equations are derived to solve the position of the link mechanism. The value of Jacobian matrix determinant equals to 0, so that the discriminative formulas of the dead-center positions are derived and the dead-center position solutions are gained. Finally, the effectiveness and accuracy of this method are verified by contrasting with traditional numerical methods.
- efficiency /
- Jacobian matrices /
- kinematics /
- mathematical models

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参考文献(11)

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