SEED Unit Design - Cam Mechanisms < >

The quality of the kinematic and dynamic performance of the follower motion is one of the principal reasons for deciding to specify a particular cam law. Other factors influencing this decision are discussed in later sections of this Guide. Dynamic performance is best understood by examination of the acceleration curve, Figure 13. It must be smooth and continuous for shockfree operation of a DRD or DFD action with zero magnitude at both start and end of the motion as well as the position of maximum follower velocity. Therefore the third derivative of follower displacement with respect to time (the "jerk") must always be finite. The conditions are defined by the boundary conditions defined in equations (14) for DRD actions. The same principles apply to DFD actions.

DRD Actions.

These conditions are met in the cases of the 3-4-5 polynomial and Modified Sinusoidal Acceleration motions, but not SHM. However, comparison of these acceleration curves shows that the peak follower acceleration is least for a given lift and segment angle with SHM.* The last is particularly suitable for reversing the velocity at the maximum displacement of a DRFD action by blending with another motion (which should satisfy conditions (14) for the start and finish of the movement) to satisfy the boundary conditions:

* The "Constant Acceleration" cam law has an even lower peak acceleration, but subjects the follower to 3 impacts (infinite jerk) during every motion segment.

DRFD Action.

Choice of motion is also influenced by the maximum resultant force at the cam-roller interface and by manufacturing considerations. The 4-5-6-7 polynomial motion (Appendix D) is derived from boundary conditions for a DRD motion, equations (14), adding the requirement of zero jerk at w = 0 and w = 1.

Use the spreadsheet to compare the displacement curves for modified sinusoidal acceleration motion and both the 3-4-5 and 4-5-6-7 polynomial cam laws over the range 0 5 ¾ u ¾ 0.1 with the positioning accuracy of a CNC machine-tool. Use, say, a rise segment angle of 100š and a lift of 30mm. Can the theoretical superiority of the 4-5-6-7 polynomial motion be achieved in practice? How do the peak accelerations compare? The rapid start and finish given by modified sinusoidal acceleration motion assists precision manufacture and is one reason why this cam law is often chosen despite the involved computation.