On the Existence of Special Cases of Input Speed Doubling Linkage Mechanisms

Abstract

A special class of planar and spatial linkage mechanisms is presented in which for a continuous full rotation or continuous rocking motion of the input link, the output link undergoes two continuous rocking motions.In a special case of such mechanisms, for periodic motions of the input link with a fundamental frequency ω, the output motion is periodic but with a fundamental frequency of 2ω. In this paper, the above class of linkage mechanisms are referred to as speed-doubling linkage mechanisms. Such mechanisms can be cascaded to provide further doubling of the fundamental frequency (rocking motion) of the output motion. They can also be cascaded with other appropriate linkage mechanisms to obtain crank-rocker or crank-crank type of mechanisms. The conditions for the existence of speed-doubling linkage mechanisms are provided and their mode of operation is described in detail. Such speed-doubling mechanisms have practical applications, particularly when higher output speeds are desired, since higher output motions can be achieved with lower input speeds. Such mechanisms also appear to generally have force transmission and dynamics advantages over regular mechanisms designed to achieve similar output speeds.

Kinematic analysis of rhomboid pressing mechanism

“…Systems of equations, geometric relations between the links of the manipulator rhomboid mechanism were analysed [2] in literature, but the kinematic parameters were not obtained. It is only claimed [3] that in these crank-crank types of planar linkage mechanisms, two turns of the input link results in one full turn of the output link when the input drive has the shortest link. On the other hand, it is claimed that rhomboid linkage (Galloway mechanism) is used for non-uniform [4] velocity transformation with average relationship 1:2.…”