﻿ CV [Constant-Velocity] Inverse Crank [Special]

# CV [Constant-Velocity] Inverse Crank

### PSMotion Special: Constant-Velocity Inverse Crank

#### CV Inverse Sinusoid

CV [Constant Velocity] Inverse Crank is similar to the Y–Inverse Sinusoid Motion-Law. This segment can be used more than once in one machine cycle, whereas the Y-Inverse-Sinusoid can be used only one time.

The 'Y Inverse Sinusoid' is available to maintain backward compatibility.

We urge you to use the CV [Constant Velocity] Inverse Crank in preference to the Y-Inverse Sinusoid.

This segment is best explained when you imagine a rotating 'crank'.

The imaginary crank makes a full rotation in each machine cycle, but it does not rotate at constant velocity.

Imagine the motion of the tip of the crank is projected along a line, for example the X-axis.

When a Crank rotates with constant angular velocity, the motion of the tip projected on to the X-axis is 'Simple-Harmonic-Motion'.

When you apply the 'Constant-Crank-Velocity' Motion-Law to the Crank, so it does not rotate with a constant angular velocity, the motion of the tip can be made to move along the X-axis with a constant linear velocity for a portion of the crank's rotation.

However, the point can be projected on to any line, not necessarily the X-axis.

In the Blend-Point Editor:

You cannot specify any motion-derivative directly. This is because the values of the motion derivatives at the start and end of this Motion-Law are a function of the Segment-Parameters.

In the Segment Editor - see image below with Segment-Parameters

You can set the:

 • Minimum Velocity
 • Start Angle
 • End Angle

See schematic below

If you use the Flexible-Polynomial Segment before and after this segment, you can:

 • Use the Blend Control Button to make the End of the Flexible-Polynomial Segment match the start of this Segment.
 • Use the Blend Control Button to make the Start of the Flexible-Polynomial Segment match the end of this Segment.

Example Segment Parameters for a Constant Crank Velocity Segment Type.
You can edit the Angles 2,4 and 5.

Schematic of Crank (green) made to give a constant linear velocity between the Start Angle(4) and End Angle(5).
You can edit the angles 2, 4 and 5 in the Segment Editor.

In the Segment Editor, edit the:

 • Minimum Velocity [Angle of Minimum Velocity]

This parameter gives the angle, from the initial angle* of the Crank (or Rocker), at which the angular velocity of the Crank is at a minimum. At all other positions, within the angular range of this segment, the angular velocity of the Crank is more than the Minimum Velocity.

In full, we call this parameter the 'Angle of Minimum Velocity'.

The direction of the Constant-Velocity vector for the Point on the Crank is projected onto a Line that is perpendicular to the Angle of Minimum Velocity.

*The initial angle of the Rocker is given by the Base-Value of the Motion Dimension for the Crank/Rocker, not by the end of the Previous-Segment.

 • Rel Start [Relative Angle before the Minimum Velocity Angle]

This parameter gives the angle from the Angle of Minimum Velocity at which the Constant-Velocity for the Point on the Crank starts.

Usually, this angle is a negative angle.

 • Rel End [Relative Angle after the Minimum Velocity Angle]

This parameter gives the angle from the Angle of Minimum Velocity at which the Constant-Velocity for the Pointends.

Usually, this angle is a positive angle.

The velocity of the Point when projected on to the Line is constant while the crank moves within the angular range of:

Start Angle = + -

...to...

End Angle = + +

The linear velocity and the length of the Constant-Velocity of the Point along the line depends on the:

 • Segment-Width
 • Length of the Rocker/Crank
 • Segment-Parameters Rel Start Angle + Rel End Angle.

An example motion with four segments.

Segment 1:

 • Is the 'Constant-Crank-Velocity, from 0 to 73º along the X–axis
 • The Constant-Crank-Velocity Parameters are:
 o Angle of Minimum Velocity = 0º
 o Relative Start Angle = -30º
 o Relative End = 30º

With these Parameters:

 o The Y–axis Value is -30º, when the Master Machine Angle (MMA) is 0º
 o The Y–axis Value is 30º when the Master Machine Angle is at 73º

The Velocity, Acceleration and Jerk at the end of the Previous-Segment are made to match Start of this Segment.

The Position at the end of the Previous-Segment (the end of the Motion) is usually = 'Position at Start + 360º'

This makes sure the Crank rotates one time for each for each Machine Cycle

Segment 2:

 • Is a 'Flexible-Polynomial' Motion-Law, from 73 to 180º along the X–axis
 • All of the motion derivatives are made to Match the end of the Constant-Crank-Velocity Segment.

Segment 3:

 • Is the 'Constant-Crank-Velocity, from 180 to 253º along the X–axis
 • The Constant-Crank-Velocity Parameters are:
 o Angle of Minimum Velocity = 0º
 o Relative Start Angle = -30º
 o Relative End = 30º

With these Parameters

 o The Y–axis Value is 150º, when the Master Machine Angle (MMA) is 180º
 o The Y–axis Value is 210º when the Master Machine Angle is at 253º

Segment 4:

 • Is a 'Flexible-Polynomial' Motion-Law, from 253 to 360º along the X–axis
 • All of the motion derivatives are made to Match the end of the Constant-Crank-Velocity

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