Analysis of equivalent motion for stable contact in clearance-affected revolute joints

Establishing an error model for clearance-affected revolute (CR) joints that accounts for contact forces is crucial for static and quasi-static mechanism accuracy analysis. This study begins with a force analysis of CR joints, classifying 13 contact modes into stable and unstable categories based on the absence or presence of specific terms in the static equilibrium equations. A kinematic formula for equivalent motion error vectors and the fundamental properties of CR joints during contact are utilized to analyze stable contact modes, deriving geometric constraints and motion error vectors. The relationship between the ranges of contact parameter and stable contact modes is further established, revealing continuous transition patterns between stable modes. By employing screw theory and the product of exponentials formula, a kinematic mapping is formulated to relate stable contact modes, motion error vectors, error twists, and actual poses. Finally, the proposed equivalent motion error model is applied to evaluate actual poses in CR joints within the isosceles trapezoidal Bricard linkage and Sarrus linkage. This work lays the foundation for kinematic-based accuracy analysis of static and quasi-static mechanisms.