Synthesis of conjugate surface by centrodes of four-bar linkage

This paper presents an ICR-constrained, centrode-based parametric synthesis framework that generates conjugate and ruled surfaces from both standard and crossed four-bar linkages while explicitly confining the instantaneous center of rotation (ICR) to a prescribed surface. The method computes the input–output angular law and the associated base and rolling curves directly from the fixed and moving centrodes, and it implements a geometry-based selection rule to choose the conjugate-surface pair that best fulfills the motion-transmission requirements. Across representative interior- and exterior-rolling cases, the study yields four salient results: (i) exterior rolling provides larger and more nearly monotonic output-angle ranges ψ ( φ ) , whereas interior rolling offers smoother local slopes that favor linear-like transmission; (ii) excluding a guard band around the ICR-at-infinity angles and operating in two compact input-angle intervals stabilizes velocity transmission and bounds centrode extents; (iii) centrode convexity and limited curvature variation correlate with manufacturable ruled surfaces (reduced tool reorientation and lower waviness); and (iv) a curvature-based screening criterion improves robustness with respect to modest geometric deviations. These findings, together with the end-to-end computational implementation, deliver a practical pipeline for function generation and conjugate/ruled-surface design using four-bar linkages. • Parametric synthesis of four-bar linkages via fixed/moving centrodes. • ICR confined to a predefined region by four geometric parameters (R, r, α , β ). • Closed-form φ – ψ relation derived; singularities detected and excluded. • Families of conjugate ruled surfaces generated from centrode pairs. • Algorithm enables rapid exploration and datasets.