Clearance-induced output position uncertainty of planar linkages with revolute and prismatic joints

The paper presents the first kinematic model to quantify the effects of the joint clearance stack up on the nominal output link position of linkages containing revolute and prismatic joints. It demonstrates the modeling of each joint clearance, how the clearance stacks up is formed, and how the position uncertainty is affected by each joint clearance as well as the combination of all joint clearances. The novelty lies on the simplicity of the kinematic model resulted from the use of Ting's rotatability laws. For the worst case scenario, a chaotic clearance induced output uncertainty analysis at a nominal position of an N-bar linkage is reduced to a simple four-bar linkage analysis. The treatment is valid for all single loop N-bar linkages containing revolute and prismatic joints. The proposed kinematic model is showcased with a slider crank mechanism and an inverted slider crank mechanism.