﻿ CV [Constant-Velocity] Inverse Crank [Special]

# CV [Constant-Velocity] Inverse Crank

### Constant-Velocity Inverse Crank

CV [Constant Velocity] Inverse Crank is similar to the Y–Inverse Sinusoid Motion-Law.

We urge you to use this motion-law in preference to the Y-Inverse Sinusoid.

This segment can be used more than once in one machine cycle, whereas the Y-Inverse-Sinusoid can be used only one time.

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 the Crank rotates with constant angular velocity, the horizontal* motion of a Point at the end of the Crank is 'Simple-Harmonic-Motion' [ a Sine function]

When you apply the 'Constant-Velocity Inverse-Crank' segment to a Crank, the Point can be made to move with a constant linear horizontal* velocity for a portion of the crank's rotation. Thus, the crank can make a full rotation in each machine cycle, but it does not rotate at constant velocity.

* Actually, the motion of a Point on a Crank projected on to any line is Simple-Harmonic-Motion.

#### SEGMENT-EDITOR

In the Segment Editor - see image below with Segment-Parameters   You can set the:

 • Minimum Velocity • Start Angle • End Angle 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 Point ends.

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

Tutorial and Reference Help Files for MechDesigner and MotionDesigner 13.2 + © Machine, Mechanism, Motion and Cam Design Software by PSMotion Ltd