Reliable contact-state identification is essential for predicting the dynamic response of multibody systems with revolute clearance joints. Existing kinematic models remain restricted by profile assumptions. The geometric center method is applicable only to circular joints, the discrete point method requires a circular pin, and the curvature center method (CCM), although applicable to noncircular bushings and pins, may become unreliable when both contacting profiles are represented by discrete or highly irregular point sets. In such cases, the required geometric contact condition may not be satisfied by any pre-discretized point on the pin profile, leading to contact misdetection, nonphysical penetration, and distorted vibration responses. To overcome this limitation, this paper proposes a robust interpolated collinearity method for revolute clearance joints with noncircular and irregular profiles. The method retains the geometric foundation of curvature-center-based contact analysis, but replaces the search for a pin-side contact point on a pre-discretized contour by a spline-interpolation-based construction of the corresponding point. In this way, the geometric contact criterion is enforced in a continuous sense even when the pin profile is available only as a discrete point set. The proposed method is incorporated into a standard three-state clearance-joint framework and assessed through a slider–crank mechanism under several profile configurations, including elliptical and complex wear-like geometries. The results show that the proposed method remains consistent with analytical-reference solutions in smooth-profile cases, while substantially improving robustness for discrete and irregular profiles. In particular, it significantly reduces contact misdetection, avoids unrealistic penetration artefacts observed in CCM, and yields more physically consistent displacement, velocity, and acceleration responses. The proposed method therefore provides a robust kinematic framework for the dynamic analysis of revolute clearance joints with practical non-ideal geometries.