﻿ Simple-Harmonic Motion-Law

# Simple-Harmonic Motion-Law

### Simple Harmonic Motion Cam-Law, Motion-Law

#### Motion-Values: With the SEGMENT-EDITOR or the BLEND-POINT EDITOR, you ...

CAN specify the:

 • Position at the START of the segment.

CAN specify the:

 • Position at the END of the segment.

CANNOT specify the:

The Velocity values at the Start and End are [they are 0 units/s ]

The Acceleration values at the Start and End [ they are 0 units/s2 ]

The Jerk values are a function of the Positions at the Start and End of the segment, and its duration.

#### Motion-Law Coefficients

 • Velocity Coefficient: Cv = 1.571
 • Acceleration Coefficient: Ca= 4.935
 • Maximum Jerk Coefficient: Cj= -15.503
 • Jerk at Cross-over, Coefficient: Cj(co) -15.503

#### Application Notes

This Motion-Law has been used commonly in the past, principally because it creates the lowest maximum nominal follower velocity of all the Traditional Motion-Laws. However, it also produces infinite jerk at the start and end.

This makes it a poor choice form a dynamic viewpoint if you use it between Dwell Segments.  However, you can usefully apply it between Flexible-Polynomial segments, for example, so that Acceleration Discontinuities at its start and end are not realized.

Dynamic Performance:

This law should only be used in applications where inertia loading is not very significant. For values of period ratio less than 10, the use of this law will give rise to shock loading, noise and vibration during operation.

The actual acceleration at the load being driven by this Motion-Law will always be significantly higher than the nominal value, and for this reason, this segment should only be used in mechanical applications where inertia effects are insignificant.

Pressure Angle Considerations:

This is one of the Traditional Motion-Laws that produce a relatively small pressure angle - and so might allow a smaller cam for a given lift.

Drive Torques:

When considering drive torques in isolation, the nominal torque for this Motion-Law is the best of Traditional Motion-Laws - it has both the lowest value and the smoothest variation throughout the segment. For compliant systems of high speed systems (period ratio between 2 and 10) the Modified Sine and the Cycloidal are preferred.

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