Solution Method of Common Constraint of the Mechanism in the Modified G-K's Formula

Xu Zhaotang

doi:10.16578/j.issn.1004.2539.2023.04.011

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Solution Method of Common Constraint of the Mechanism in the Modified G-K's Formula

Design· Calculation | 更新时间：2023-05-04

- Solution Method of Common Constraint of the Mechanism in the Modified G-K's Formula
- Journal of Mechanical Transmission Vol. 47, Issue 4, Pages: 74-78(2023)
- 作者机构：
  
  三江学院机械与电气工程学院，江苏南京 210012
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2023.04.011
  CLC：
- Published：15 April 2023，
  
  Received：14 March 2022，
  
  Revised：25 April 2022，
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许兆棠.修正的G-K公式中机构公共约束的求解方法[J].机械传动,2023,47(04):74-78.

Xu Zhaotang.Solution Method of Common Constraint of the Mechanism in the Modified G-K's Formula[J].Journal of Mechanical Transmission,2023,47(04):74-78.
许兆棠.修正的G-K公式中机构公共约束的求解方法[J].机械传动,2023,47(04):74-78. DOI： 10.16578/j.issn.1004.2539.2023.04.011.

Xu Zhaotang.Solution Method of Common Constraint of the Mechanism in the Modified G-K's Formula[J].Journal of Mechanical Transmission,2023,47(04):74-78. DOI： 10.16578/j.issn.1004.2539.2023.04.011.

摘要

在机构自由度的计算中，采用修正的Grübler-Kutzbach的机构自由度计算公式时，需要求解机构的公共约束。为了用更简单的方法获得机构的公共约束，在定义机构公共约束的基础上，先根据运动副的自由度和绝对运动不为零的运动副约束方向，得到机构没有公共约束的坐标方向；再在其余的坐标方向上确定机构的公共约束。有、无机构公共约束的坐标方向数共为6。机构的公共约束等于有公共约束的坐标方向的个数。该方法不用螺旋理论求解机构的公共约束，方便了工程技术人员求解，也方便了修正的Grübler-Kutzbach的机构自由度计算公式在工程技术人员中得到推广和应用。

Abstract

In the calculation of mobility of the mechanism using the modified Grübler-Kutzbach's formula of mechanism mobility

the common constraint of the mechanism has to be solved. In order to obtain the common constraint of the mechanism with a simpler method and on the basis of defining the common constraint of the mechanism

the coordinate direction of the mechanism without common constraint is obtained according to the mobility of kinematic pair and the constraint direction of the kinematic pair whose absolute motion is not zero

and then the common constraint of the mechanism is determined in other coordinate direction. The total number of coordinate directions with and without the common constraint of the mechanism is 6. The common constraint of the mechanism is equal to the number of coordinate directions with common constraint. This method does not need the screw theory to solve the common constraints of the mechanism

which is convenient for engineering and technical personnel to solve the common constraints of the mechanism. It is also convenient for the modified Grübler-Kutzbach's formula of the mechanism mobility to be popularized and applied in engineering and technical personnel.

关键词

机构自由度公共约束运动副的自由度运动副的绝对运动坐标方向

Keywords

MechanismMobilityCommon constraintMobility of kinematic pairAbsolute motion of kinematic pairCoordinate direction

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