Force analysis as a support to computer-aided tolerancing of planar linkages

• A method is proposed for tolerance analysis of planar linkages.
• Stackup coefficients are calculated by solving a force analysis problem.
• Trusses and mechanisms with lower pairs and no overconstraining are treated.
• Complex problems are tackled by finite element software.

The paper proposes a method for tolerance analysis on planar structures and mechanisms. As for generic assemblies, deviations on a functional requirement involving different parts are calculated from tolerance specifications on individual part dimensions. For a linkage the requirement is usually the position or orientation of a given element (link, joint) with respect to a fixed frame, and the solution of the problem has some additional difficulties such as the correct treatment of joint clearances. The paper points out that, for underconstrained or exactly constrained linkages, tolerance analysis can be treated by analogy with a force analysis problem. The static analogy is first introduced and justified from well-known concepts of classical mechanics, and then translated into a calculation procedure that is able to evaluate the propagation of deviations from different types of dimensions (lengths of links, diameters of pins and holes at joints), as well as from linear and angular actuators. Problems of high complexity are shown to be easily solvable by the proposed method by means of available software tools for the structural analysis of planar frames and trusses.