关键词: 几何约束, 解耦性分析, 冗余约束, 几何推理

Abstract: It is a key problem to solve the geometric constraint system between two rigid
bodies(GCSBTRD) efficiently and stably when 3D geometric constraint system has been
decomposed into a series of GCSBTRDs using equivalent constraint substitution method. In this
paper, the decoupling conditions to separately solve angle constraints and distance constraints of
GCSBTRDs are presented after analyzing the parametric structure of angle constraints and
distance constraints. Then, with the geometric analysis of GCSBTRDs, it is found that the
GCSBTRDs consisting of the geometric constraints with more than one constraint degrees can be
divided into dozens of patterns, which can all be solved analytically by geometric reasoning
method. Subsequently, the adverse impact on numerical solution of GCSBTRDs from additional
direction constraint, redundant constraint and contradictory constraint is addressed to demonstrate
the advantage of geometric reasoning method. Finally, a hybrid solving strategy based on the
classification of constraint combinations is proposed to solve GCSBTRDs, whose effectiveness
has been validated by a practical example.

Key words: geometric constraint, decoupling analysis, redundant constraint, geometric
reasoning