Form-closure of planar mechanisms: Synthesis of number, configuration, and geometry of point contacts

This paper presents a study on restraining the motion of planar mechanisms using point contacts between the links of the mechanisms. First-order form-closure (FFC) and second-order form-closure (SFC) of 1- and 2-degrees-of-freedom (d.o.f.) smooth planar motions are studied. It is shown geometrically that two and three point contacts are sufficient for FFC of an object which is capable of executing 1- and 2-d.o.f. motions respectively. These results are applied for FFC of planar mechanisms. A theory for contact curvature based SFC of 1- and 2-d.o.f. motions with a single point contact is presented. It is derived that the instantaneous point-path curvature of points on a specific line of a 2-d.o.f. moving plane is always bounded. Using this result, a procedure is chalked out for immobilizing 1- and 2-d.o.f. mechanisms with a single contact. Illustrations of immobilizing four-bar and 2R-mechanisms are presented. Rapid prototyped model of the four-bar mechanism and stoppers is fabricated and the SFC theory is verified.