A Traditional Motion-Law. Its name is often reduced to Mod-Sine.

A motion with continuous Velocity and Acceleration, from start to end. The Jerk is finite at its start and end.

It is commonly used in high-speed mechanisms. It is the most common motion-law used with Cam Indexing mechanisms.

Its Drive Torque is relatively low and it reverses its sign most gradually of all the Traditional Motion-Laws.

Start Position - which usually flows from the End-Position of the Previous-Segment

End Position

Start Velocity and End Velocity

Start Acceleration and End Acceleration

Start Jerk and End Jerk

None

Start-Range

End- Range

0 ≤ Start-Range < End-Range ≤ 1

Velocity Coefficient :

Acceleration Coefficient :

Jerk Coefficient :

Jerk at Crossover :

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 crossover (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.

The Acceleration function is a series of Sinusoid functions.

•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.