﻿ Motion-Law: Modified Sinusoid

# Modified-Sinusoid Motion-Law

### Modified-Sinusoid Cam-Law, Motion-Law

Modified-Sinusoid is a Traditional Motion-Law. It is frequently used with Indexing Cam Mechanisms.

#### Segment-Editor AND Blend-Point Editor

CAN specify the:

 • Position at the START of the segment.

The Position value usually flows from the Previous-Segment.

CAN specify the:

 • Position at the END of the segment.

CANNOT specify the:

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

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

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

Notes:

 • The  Velocity and Accelerations are zero at its Start and End
 • The  Jerk values are not zero but 'finite' at its Start and End
 • The Segment is acceleration is symmetrical. #### Modified Sine Motion-Law

It is Symmetrical.

It is trigonometric functions in acceleration, with:

 • a ¼ sine wave function, starting from zero acceleration, for 12.5% of the Segment-Width
 • a ½ cosine function, for 75% the Segment-Width
 • a ¼ sine wave function, returning to zero acceleration, for 12.5% of the Segment-Width

#### Motion-Law Coefficients

 • Velocity Coefficient: Cv = 1.76
 • Acceleration Coefficient: Ca= 5.53
 • Maximum Jerk Coefficient: Cj= +69.47
 • Jerk at Cross-over, Coefficient: Cj(co) -23.15

#### Application Notes

This law produces finite jerk throughout the segment. It also produces a relatively low nominal peak velocity, but a relatively high peak nominal acceleration. This Motion-Law also has a relatively low jerk value at the cross-over point (the mid-point).

Dynamic Performance

This Motion-Law is recommended in applications where the period ratio is between 5 and 10, particularly where the input drive is flexible and has backlash present. It also performs relatively well from a residual vibration viewpoint.

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 and pre-prescribed maximum pressure angle.

Drive Torques

Both the nominal drive torque characteristics and the actual drive torques for low period ratio values are very good for this law. The low peak values and smooth variation of the drive torque during the motion segment further emphasise the suitability of this Motion-Law in applications where the input drive is flexible or exhibits backlash.

It also needs very low overall Power. Hence it is very efficient for servo applications.

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