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 part, e.g. a Crank. There can be only one segment in each motion.

The Constant-Velocity Inverse Crank, a very similar motion-law, can have more than one segment in each motion.

Motion-Description

This segment is best explained by considering the motion of a Point at the end of a Crank that is projected onto a Line.

When a Crank rotates with Constant angular velocity, the projected motion of the Point on the Line is Simple-Harmonic-Motion.

When you use Y-Inverse-Sinusoid, the projected motion of the Point on the Line is Constant Linear Velocity.

Motion-Values

You CAN specify the

Start-Position - defined by the three Segment-Parameters - see below.

End-Position - defined by the three Segment-Parameters - see below.

You CANNOT specify the:

Velocity at the Start or End

Acceleration at the Start or End

Jerk at the Start or End

See Note below, and example.

Segment Parameters

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 ...

AngleRed-14-6 is to Blue line relative to any other line, as defined by the Base-Value of the Motion-Dimension FB.

Radius of Rocker* (Example is 100mm)

The Radius of the Rocker (rotating-Part) specifies the minimum and maximum distance from the rotating-axis of the Green point, at the end of the Rocker, projected onto the Blue line.

Start-PositionRed-14-1b (Example SP=-50mm)

Directional Distance from the rotating-axis of the Green point projected onto the Blue line when the Green point starts to move with Constant-Velocity along the Blue line.

End-PositionRed-14-2 (Example EP = -50mm)

Directional Distance from the rotating-axis of the Green point projected onto the Blue line when the Green point ends moving with Constant-Velocity along the Blue line.

MechDesigner calculates angles Red-14-4 and Red-14-5 for the Rocker relative to the Blue Line, from the Start-Position and End-Position.

Note:

The Crank rotates Counter-Clockwise when Start-Position is a Negative and End-Position is a Positive.

The Crank rotates Clockwise when End-Position is a Negative and Start-Position is a Positive.

Segment-Range

Start-Range

End- Range

0 ≤ Start-Range < End-Range ≤ 1

 

Video: Y-Inverse-Sinusoid Example
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.