Kinematic analysis of quick-return mechanism in three various approaches

Mechanismshavebecomeapartofourlifeandaretobefound not only in technical practice, but along every step ofoureverydaylife[1,2,6].Theyhelpustodoourworkmoreeasilyandmorecomfortably.Themechanismisusuallyapartofamachinewheretwoor more pieces are combined, so that the motion of the firstcompels the motion of the others, according to a lawdepending on the nature of the combination. The operationofanymachinedependsupontwothings:1. the transmission of certain forces,2. the production of determinate motions.Indesigning,dueconsiderationmustbegiventobothofthese, so that each part may be adapted to bear the stressesimposed on it, as well as have the proper motion relative totheotherpartsofthemachine.The structure that supports the moving parts andregulates the path motions, or kind of motion, is called theframe of a machine [3]. In discussing the motions of themoving parts, they are considered in regard to the frame.The frame absorbs the forces or moments that originate atthe transformation of motions [7]. The components whichactuate the mechanism are called the drivers, the othercomponents whose motions are caused are called thefollowers.It is often needed to define the velocity and accelerationof a rigid body or some point of mechanism inmanufacturingpractice,iftheinputparametersofdriverareknown. The kinematic analysis is concerned with theproblemslistedbelow.The goal of the kinematic analysis is to investigate themotion of individual components of a mechanism (or itschosen points) in dependence on the motion of drivers. To