Mechanisms of P. L. Chebyshev

P. L. Chebyshev's works in the field of practical mechanics are not as widely covered in the literature as his work in mathematics. But he deserves the credit for the scientific formulation and brilliant solution of a number of problems in one of the most difficult problems of the mechanisms theory - the problem of mechanisms synthesis.
The following problems of synthesis of approximate guiding mechanisms are considered in this report: synthesis of hinge mechanisms with stops, hinge mechanisms for reproducing two rocking of the rocker arm in one crank rotation, hinge mechanisms for transmitting rotational motion. The properties of connecting rod curves with axial symmetry are used in order to solve these problems. The mechanisms described are built on the basis of a lambda-mechanism. One of the lambda-mechanism vertices trajectories can represent various plane curves: approximate line segments, circular arcs, eights, ellipses. The "paradoxical" Chebyshev mechanism is considered in more details. There are six singular points in the configuration space of this mechanism, which are traversed with a full rotation of the handle. The dynamics of "paradoxical" mechanism is studied for some small perturbation of the parameters of mechanism.