基于一种自由度新理论的过约束判断方法

Method for Determination of Overconstraint Based on a New Mobility Theory

过约束判断是机构自由度计算的关键,也是瓶颈。为使过约束判断更简单、快速,从其产生的本质出发,考虑约束的相关性,基于一种新的自由度理论,提出结合杆组参数矩阵进行过约束判断的方法。针对夹角不为零的平行R杆组(具有平行转动轴线的杆组)位移参数确定问题,提出参数垂直分量有效法则,使考虑不同几何空间下的螺旋相关性问题转化为仅考虑平行约束的相关性判断问题。将过约束的产生归纳为三类情况,分析各类情况下过约束的数目及类型,总结过约束中公共约束判断和并联冗余约束判断的原则。以一个典型机构为例,利用上述方法对其过约束数目和性质进行求解,以进一步验证所提法则、方法的合理性和实用性。

Overconstraint determination is the key and bottleneck of mobility calculation. Starting from its engendered nature, the linear dependence of constraint, a novel approach to overconstraint determination combined with linkgroup parameter matrix is presented to make it easier and faster based on a new mobility theory. To ascertain displacement parameters when the angle of parallel R link group （linkgroup including revolute joints with parallel rotation axis） is not zero, the validity of its vertical component is proposed which only takes parallel constraints of screw linear dependence into account in the midst of varied geometric spaces. The number and types of overconstraint arc analyzed in three different situations which derive from its generation. Meanwhile the principles of common constraint and parallel-redundant-constraint determination arc concluded. A typical mechanism is taken as an instance and elicited the number and characters of its overconstraint applying the above approach to further verify the rationality and applicability of the proposed approach and principles.