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    Abstract In this paper a kinematic analysis of an adjustable slider-crank mechanism is presented. The proposed mechanism is formed by an output member, i.e. The slider, by a connecting rod and by an equivalent crank mechanism, consisting of a pair of identical gears and a connecting link assembled in a typical epicyclical configuration. One point of the planet gear moves along an epicycloidal path,while the other gear is held stationary and the planet arm rotates around a fixed hinge. Such epicycloidal motion is converted into a reciprocating motion of the slider by means of the connecting rod, as in a traditional slider-crank mechanism.By holding the planet arm stationary and modifying the relative angular position of the two gears, an adjustment of the entire mechanism is achieved, in such a way that, if the arm is allowed to rotate again, the slider starts moving according to a different law of motion.
    Keywords: Adjustable mechanism, slider-crank mechanism, variable stroke22878
    Introduction
      One goal of mechanical engineers in the analysis and synthesis of mechanical systems is the design of a mechanism for function, path or motion generation. In many industrial applications, where flexibility is one of the system requirements,programmable manipulators are used to accomplish a wide variety of output mo dons. A less flexible but simpler and more reliable solution is represented by adjustable mechanisms. Basically, these mechanisms are single degree-of-freedom(d.o.f.) systems, with one or a few adjustable parameters, which can be referred to as control inputs.
      Several analytical or graphical methods for the synthesis of different adjustable mechanisms are proposed in literature. Based on complex algebra, McGovern and Sandor [1,2] proposed the synthesis of function and path generating mechanisms, where the location of the fixed pivot was adjustable, as to enable two sets of precision points to be generated. A technique for the synthesis of adjustable linkages was proposed by Tao and Krishnamoothy [3,4], who used a graphical approach to synthesize mechanisms for the generation of variable coupler curves, either sym- metrical and with cusps. Adjustable four-bar linkages were proposed by AhmadD. Mundo et al.and Waldrom [5], Naik and Amarnath [6] and Chang [7]. The latter proposed a procedure to synthesize adjustable mechanisms for the generation of circular arcswith specified tangential velocities. Adjustable four-bar linkages for multi-phase motion generation were proposed by Wang and Sodhi [8] and by Zhou and Chung [9], while Russell and Sodhi [10] solved the same problem by synthesizing and adjustable RRSS mechanism. Recently, Zhou [11] proposed the synthesis of adjustable function generation mechanisms, formed by a four-bar linkage with an adjustable pivot location of the driven link. By optimizing the location of the adjustable pivot, the proposed methodology can be extended to the synthesis of non-adjustable linkages for approximate function generation.
      Some research has focused on the study of adjustable slider-crank mechanisms. Zhou and Ting [12] proposed such mechanisms for multiple path generation,while Russell and Sodhi dealt with problems of multi-phase motion generation[13] and multi-phase path and function generation [14]. An attempt to extend this concept to three dimensional contexts was made by Hong and Erdman [15] and by Shoup [16]. The latter proposed the application of an adjustable spherical slider-crank mechanism in variable stroke pumping systems.
      More complex adjustable mechanisms have been studied by Russel and Sodhi[17], who proposed the kinematic synthesis of adjustable RSSR-SS mechanisms for multi-phase finite and multiply separated positions, and, recently, by Pennock and Israr [18]. Pennock and Israr investigate the kinematic analysis and synthesis of an adjustable six-bar linkage using a methodology based on the determination of kinematic coefficients.
      This paper presents an adjustable slider-crank mechanism, where a pair of identical circular gears, assembled in an epicyclical configuration, is used as an equivalent crank. This equivalent crank consists of a stationary sun gear, a moving planet gear and a moving planet arm. A connecting rod joins a point of the planet gear to the slider of the mechanism. Two modes of operation can be identified for the proposed mechanism: (i) the working mode, in which the input member of the system, i.e. the planet arm, rotates around a fixed pivot, while the central gear is held stationary; and (ii) the adjustment mode, where the planet arm is held stationary while the central gear is rotated as to modify the relative angular position be-tween the two gears. In the working mode, a point of the planet gear, which is connected to the slider by a connecting rod, moves along an epicycloidal path. The rotation of the planet arm, that is the main input of the system, is then converted into a reciprocating motion of the slider, as in a traditional slider-crank mechanism. If the relative angular position of the two gears is modified during the adjustment phase, a reconfiguration of the entire mechanism is achieved and the motion of the slider changes.
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