SEED Unit Design - Cam Mechanisms < >

The simple solution of shaping the cam profile from blending sections of circular arcs is only suitable for very low speeds because the follower velocity and acceleration are determined by the rate of change of radius from the axis of rotation to the profile. Circular arc cams have unnecessarily high accelerations and impose shock loading whenever the follower passes a blending point. Therefore cam design should begin from good kinematic and dynamic follower motion and then making the profile to produce the required follower displacement as the cam rotates.

The mathematical expressions known to produce suitable follower motions are known as cam laws. They relate the follower displacement during one motion segment to the angle of cam rotation from the start of that movement. Expressed in non-dimensional form the same equations apply to both translating and swinging-arm followers in any configuration. They also facilitate the derivation of blended motions such as Modified Sinusoidal Motion (see below) to obtain superior dynamic performance and/or to include a constant velocity portion. The curves of the non-dimensional equations for follower displacement, velocity and acceleration vs normalised cam angle are known as the cam characteristics, examples are shown in Figures. 11, 12 & 13. The cited references contain a great variety of cam laws, mostly based on trigonometrical or polynomial functions. The principles are demonstrated by the following examples. (Critical values, in non-dimensional form, are given in Appendix E for some cam laws).

Figure 11 Non-Dimensional Follower Displacement

Non-Dimensional Cam Rise Angle (u)

Figure 12. Non-Dimensional Follower Velocity

Non-Dimensional Cam Rise Angle (u)

Figure 13. Non-Dimensional Follower Acceleration.

Non-Dimensional Cam Rise Angle (u)

Modified Sinusoidal Acceleration Motion. This motion is constructed by blending the acceleration curve from sections of sine curves having the same amplitude but different periods. Smooth transition is ensured by blending at positions of zero acceleration. Then the equations for the follower velocity and displacement are found by successively integrating the acceleration equation for each portion of the complete rise or fall movement. The constants are determined by the blending requirements.

Non-dimensional follower displacement: