Tandem design of mechanisms for function generation and output speed variation

A new approach for generation of functions based on application of a multi-gear drive is proposed. The approach provides solution to the functional ψ(α)=gn(gn-1(⋯(g1(α))))ψ(α)=gn(gn-1(⋯(g1(α)))) wherein ψ(α)ψ(α) is the function assigned for generation and gi(α),i=1,…,ngi(α),i=1,…,n, is the transmission function of pair i of conjugated non-circular gears. The specifics characteristics of the proposed approach are: (a) integrated impact by application of n synchronized gear drives, (b) favourable shape of centrodes, and (c) observation of limits of pressure angle. In addition to the approach for function generation, tandem design for the following types of planar linkages has been developed: double-crank linkage, crank-slider linkage and Scotch–Yoke mechanism. Tandem design for mechanism formed by a rack and non-circular gear has been developed as well. The developed theory is illustrated with seven detailed numerical examples.