Synthesis of Stationary Cams

Abstract

This paper presents a method for designing stationary cams with constant speed roller followers. A stationary cam is immovable, but it guides its follower to produce a desired motion with the follower being driven by other links. In order to avoid infinite jerk of the follower motion, the pitch curve of a stationary cam should consist of pieces of transition curve, which provide gradual change in curvature and are interposed between straight lines and circular arcs. The general parametric equations of transition curves are derived and the cam design process is demonstrated. This method is applicable for designing the guideways of tool magazine in automatic tool-changing system of the machine center.

Design of backlash-free straight-curved guide devices

“…As will be illustrated later, the first side profile can further be designed to smoothly guide both rollers to produce a desired motion while the pitch curve of the rollers can avoid sudden changes in curvature. 11 The rail profile and the path of cutter center Figure 5 shows the slider contacting the connection rail section in an arbitrary position. Roller centers A and B share a common pitch curve that is composed of a straight line and a circular arc of radius R 1 tangentially intersecting at point T. As point A moves along the straight line and point B moves along the circular arc, the motion of link AB is kinematically equal to that of the coupler link of a common slidercrank mechanism.…”

“…Then, the coordinates of roller center C(X C , Y C ) can be obtained from equations (10) and (11). The instant center I 12 between the slider and the rail can be located by inspection and can be expressed as Figure 6.…”

“…As a third point of the slider, the coordinates C (X C , Y C ) of roller center C can be calculated by applying equations (10) and (11).…”

“…As shown, tc is always larger than ts with a magnitude of R1-R1 2-(lsinη2false)2, and thus the connection rail section needs to have a varying thickness in this device. Designing the profiles of the connection rail section is similar to designing the cam profiles of a conjugate stationary cam mechanism, 11,13 and the same approaches can be extended here to design the profiles of the connection rail section.…”

“…A curvilinear guide device can be considered as a stationary cam mechanism 10,11 whose slider may have various types, similar to various followers of a cam mechanism. If the employed slider is equipped with only two rollers, it will not be able to simultaneously support horizontal, vertical, and moment loads.…”