Motion-Law: Y–Inverse-Sinusoid

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Motion-Law: Y–Inverse-Sinusoid

Y–Inverse-Sinusoid

Note: This Motion-Law is usually applied to a Rotating Crank.

You can use this segment one time per motion.

We recommend that you use the Constant-Velocity Inverse Crank, as it can be used many times per motion.

This segment is best explained by considering the X and Y motion components of a Point that is at the end of a rotating-Part or Crank.

When a Crank rotates with Constant angular velocity, the motion of a Point at the end of the Crank that is projected onto a Line is Simple-Harmonic-Motion ( a Sine function )

When you apply the Y–Inverse Sinusoid segment to a Crank, the motion of a Point at the end of the Crank that is projected onto a Line can be made to move with a constant linear velocity for a phase of the Crank's rotation.

 

Y-Inverse-Sinusoid

Example Segment Parameters

Example Segment Parameters

Schematic of Crank made to give a constant linear velocity from Angle(4) (defined by Start-Position(1), to Angle(5), defined by the End-Position(2).

Schematic of Crank made to give a constant linear velocity ...

Schematic of Crank made to give a constant linear velocity from angleRed-14-4, defined by Start-PositionRed-14-1, to angleRed-14-5, defined by the End-PositionRed-14-2.

MechDesigner calculates anglesRed-14-4 and Red-14-5. AngleRed-14-6 is the Base-Value in the Motion-Dimension FB.

Use Segment-Parameters to enter the Start-Position, End-Position, and  is the Radius of the RockerRed-14-3.


Segment Parameters.

Radius of Rocker* (Example is 100) (* When the Rocker rotates for a full rotation, we can also use the term Crank).

The Radius of the Rocker specifies the minimum and maximum range of positions when projected onto a Line.

Start-Position (Example SP=-50) (Note: Do not confuse this with the Start-Position in the Segment-Editor)

Position of the Point that is projected onto a reference Line when it start to move at Constant-Velocity.

MechDesigner calculates the Angle of the Crank to give this distance, relative to the Reference Line of the Crank.

End-Position (Example EP = -50)  (Note: Do not confuse this with the End-Position in the Segment-Editor)

At the end of the Constant-Velocity, End-Position specifies the distance from the end of the Crank to its Center, when projected onto the reference Line* of the Crank.

MechDesigner calculates the Angle of the Crank to give this distance, relative to the Reference Line of the Crank.

Y-Inverse Sinusoid

Y-Inverse Sinusoid

Example: with two segments.

Crank rotates in a Counter-Clockwise direction

Constant-Velocity Starts at 50mm to Left of Crank-Center (angle 120º)

Constant-Velocity Ends at 50 to Right of Crank-Center (angle 60º)

Segment 1:

X-axis Start = 0 ; End = 90º

The Y–Inverse Sinusoid Segment-Parameters are:

Radius of Rocker = 100mm, Start Position = -50, End Position = 50mm.

With these Segment-Parameters:

The Y–axis is 120º†, when the Master Machine Angle (MMA) is 0º .

The Y–axis is 60º, when the Master Machine Angle is 90º .

Segment 2:

X-axis Start = 90º, End = 360º (0º)

A Flexible-Polynomial

The Y–axis is 60º, when the Master Machine Angle is 90º (= end of Segment 1)

The Y–axis –240º when the Master Machine Angle is 360º .

Thus the Crank makes a full rotation from +120 to -240 in a counter-clockwise direction.