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The outline of the paper is as follows: in section 2, the mathematical model for the kinematic analysis of the proposed mechanism is introduced. The output motion is expressed as a function of the main input of the system, i.e. the rotation the planet arm, and is parameterized with respect to the control input, i.e. the relative angular position between the two gears. In section 3, an example is illustrated to show the effectiveness of the proposed strategy for the adjustment of the slider motion. Some concluding remarks are provided in section 4.Kinematic Analysis of an Adjustable Slider-Crank Mechanism.
Kinematic analysis of the adjustable slider-crank mechanism
In figure 1 the proposed adjustable slider-crank mechanism is schematically represented in the working mode. An equivalent crank mechanism is formed by two identical circular gears: the first gear, centered in point O,, is held stationary,while the second gear, centered in point OZ, is forced to an epicyclical motion by the planet arm, which represents the input member of the system. While this link is rotated by an angle φ{0,2Π} rad, one point A of the planet gear moves along a
closed trajectory, specifically an epicycloid.
If point A on the planet gear and point B on the slider are connected to each other by a connecting rod, the input motion, i.e. the rotation a of the planet arm,is converted into a reciprocating motion of the slider, as in a classical slider-crank mechanism.
In this section, the mathematical model for the kinematic analysis of the proposed mechanism is derived by using the closure equation of the proposed mechanism and by analyzing the kinematic properties of the gear train.
By referring to figure 1, the following loop equation can be written
(1)
where the vector defines the position of point A.
In this paper, an adjustable slider-crank mechanism has been proposed and the mathematical model for its kinematic analysis illustrated. By using an example,the effects of control input modifications on the output motion of the mechanism have been analyzed. The results demonstrate the proposed strategy for the adjustment of the slider motion.
Given the structural simplicity of the proposed mechanism, the authors believe that it can be employed in those applications, e.g. variable stroke pumping where the flexibility of the output motion is a requirement.
Introduction to Mechanism
Mechanisms may be categorized in several different ways to emphasize their
similarities and differences. One such grouping pides mechanisms into planar, sphe-rical, and spatial categories. All three groups have many things in common; the criterion, which distinguishes the groups, however, is to be found in the characteristics of the motions of the links.
A planar mechanism is one in which all particles describe plane curves in space and all these curves lie in parallel planes; i. e., the loci of all points are plane curves parallel to a single common plane. This characteristic makes it possible to represent the locus of any chosen point of a planar mechanism in its true size and shape on a single drawing or figure. The motion transformation of any such mechanism is called coplanar. The plane four-bar linkage, the plate cam and follower, and the slider-crank mechanism are familiar examples of planar mechanisms. The vast majority of mechanisms in use today are planar. A spherical mechanism is one in which each link has some point which remains stationary as the linkage moves and in which the stationary points of all links lie at a common location; i.e., the locus of each point is a curve contained in a spherical surface, and the spherical surfaces defined by several arbitrarily chosen points are all concentric. The motions of all particles can therefore be completely described by their radial projections, or "shadows", on the surface of a sphere with properly chosen center. Hooke's universal joint is perhaps the most familiar example of a spherical mechanism. Spherical linkages are constituted entirely of revolute pairs. A spheric pair would produce no additional constraints and would thus be equivalent to an opening in the chain, while all other lower pairs have nonspheric motion. In spheric linkages, the axes of all revolute pairs must intersect at a point.