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本文介绍了用约束数表示的自由度公式的几个重要的发展阶段,指出了以往用环路公共约束表示的自由度公式的不足之处是:在处理含有虚约束机构时,必需通过计算虚约束数,才能得出正确的自由度结果.为克服这一缺点,本文用虚拟环路、虚拟环约束、广义副约束数等新概念,分析了构件的自由度数和运动副约束数之间的关系,给出了用虚拟环路公共约束表示的自由度公式.得出了机构自由度是机构所有构件自由度之和与所有运动副约束数之差,再加上各虚拟环公共约束之和的计算公式,以及机构总的过约束数就是各虚拟环约束数之和的重要的结论.这种用虚拟环公共约束表示的机构自由度公式,能避开虚约束的计算.通过多个计算实例,证明了虚拟环路法对自由度分析的正确性、有效性和适用性.
In this paper, we introduce several important stages of the formula for degree of freedom expressed by constraint numbers, and point out that the shortcoming of the formula for the degree of freedom expressed by the conventional constraints of the loop is that when dealing with the mechanism with virtual constraints, Constraints to obtain the correct degree of freedom results.In order to overcome this shortcoming, this paper analyzes the relationship between the degree of freedom of the component and the number of the secondary constraint by using the new concepts of virtual loop, virtual ring constraint and generalized secondary constraint number The relation between the degree of freedom expressed by the public constraint of the virtual loop is given and the degree of freedom of the mechanism is obtained as the sum of the degrees of freedom of all the components of the mechanism and the number of the constraint of all the motions, , And the total overconstraints of the mechanism are the important conclusions of the sum of the constraints of each virtual ring, which can avoid the calculation of the virtual constraint by using the calculation of the degree of freedom of the mechanism represented by the common constraint of the virtual ring, The example proves the correctness, validity and applicability of virtual loop analysis to the degree of freedom.