A Traditional Motion-Law.

Other names for this law are: Mod-Sine, and as MS in cam indexer catalogs. It may include a Constant-Velocity, e.g. MS30 - see Sine-Constant-Cosine  .

The Mod-Sine is continuous in Velocity and Acceleration and it has a relatively low Jerk at crossover. While Jerk is continuous within the motion-law, it has a greater than average Jerk discontinuity at its start and end.

Here are the Normalized Equations

Start Position

The Start Position 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 Coefficients :

Jerk Coefficient :

Jerk at Crossover :

Torque Coefficients :

The Modified Sinusoid motion-law has relatively low peak velocity, and low jerk at crossover.

Dynamic Performance

The Modified Sine is a good general purpose motion-law particularly in applications where the period ratio is between 5 and 10, and if the input drive is flexible or it has backlash. It performs well with respect to residual vibration after the segment is complete.

Pressure Angle Considerations

It produces a relatively small pressure angle, and so it can give a smaller cam for a given lift and pre-prescribed maximum pressure angle than other motion-laws.

Drive Torques

The nominal drive torque characteristics and the actual torque values are low. The low peak values and the smooth variation of drive torque further emphasize the suitability of this motion-law where the input drive is flexible or has backlash.

The Acceleration function is a series of Sinusoid functions (see equations)

•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.

You can use the Segment Range parameters and two segment, to design an Asymmetrical Motion.