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# Modified-Trapezoidal Motion-Law

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# Modified-Trapezoidal Motion-Law

### Modified-Trapezoid Cam-Law, Motion-Law

#### 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.

#### Modified-Trapezoid

Symmetrical

Continuous in Position, Velocity and Acceleration,

Finite Step of Jerk at its Start and End

Continuous in Jerk at cross-over

In acceleration, the segments are:

1/4 Sine function for 0.125 of the Segment-Width

Constant-Acceleration for 0.25 the Segment-Width

1/2 Cosine function for 0.25 the Segment-Width - crossing the mid-point of the motion law at the mid-point of this segment

Constant-Acceleration for 0.25 the Segment-Width

1/4 sine wave function for 0.125 of the Segment-Width

Motion-Law Motion-Coefficients:

Velocity Coefficient: Cv = 2

Acceleration Coefficient: Ca= 4.89

Jerk Coefficient: Cj= ±61.43 (Start, Finish and cross-over).

#### Application Notes

The Modified Trapezoidal motion law has finite jerk throughout the segment. It has an average peak nominal acceleration compared to the other Traditional Motion-Laws.

Dynamic Performance

This Motion-Law is a good general purpose type particularly in applications where the period ratio is above about 5. It is not good in applications where the input drive has backlash or is relatively flexible. As long as the drive satisfies these conditions, then this segment exhibits low residual vibrations.

Pressure Angle Considerations

This one of the Traditional Motion-Laws that produce a relatively large pressure angle - and so might need a large cam for a given lift and pre-prescribed maximum pressure angle.

Drive Torques

This Motion-Law exhibits a rapid reversal of acceleration at the cross-over (mid) point. Only the Constant-Acceleration Motion-Law is more rapid, of the Traditional Segments. It is unsuitable to drive heavy masses at high speeds. The rapid reversal of torque may give rise to severe vibrations and shock loading especially if the period ratio is less than 10.