﻿ Y-Inverse-Sinusoid [Special]

# Motion-Law: Y–Inverse-Sinusoid

### PSMotion Special: Y–Inverse-Sinusoid

#### Y Inverse-Sinusoid

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

When a Crank rotates with constant angular velocity, the horizontal* motion of a Point at the end of the Crank is 'Simple-Harmonic-Motion'.

When you apply the 'Y–Inverse Sinusoid' segment to a Crank, the Point can be made to move at a constant linear velocity for a portion of the rotation.

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

In the Blend-Point Editor, edit the:

 • Start Position. If EP is more than SP, then the Constant-Velocity motion is from left to right, not right to left

In the Segment Editor, edit the:

 • Radius of the Rocker: R

The maximum range of the Rocker = ± Radius of the Rocker.

The Radius of the Rocker specifies the maximum amplitude of the Simple-Harmonic-Motion.

 You can make this Parameter equal to the actual length of the Crank. Or, make it 100. When it is 100, the other two parameters are percentages of amplitude, R.
 • Start Position [-R ≤ Start Position ≤ R]

The Start Position must be within the maximum range.

Specifies the motion value, in X–axis Units, that the tip of the rocker is at when the crank starts to move at a Constant-Velocity

 • End Position [-R ≤ End Position ≤ R]

Specifies the motion value, in X–axis Units, that the tip of the rocker is at when the crank ends the move at Constant-Velocity.

Th End Position must be within the maximum range. Click to Expand or Collapse

If SP is more than EP, then the Constant-Velocity of the Point is from Right to Left.

If EP is more than SP, then the Constant-Velocity of the Point is from Left to Right.

An example with two segments.

The first Segment:

 • Is the 'Y–Inverse-Sinusoid' Motion-Law, from 0 to 90º along the X–axis
 • The Y–Inverse Sinusoid Segment-Parameters are:
 o Radius of Rocker = 100mm,
 o Start Position = 50,
 o End Position = -50mm.

With these Parameters:

 o The Segment Y–axis Value is 60º†, when the Master Machine Angle (MMA) is 0º .
 o The Segment Y–axis Value is 120º‡ when the Master Machine Angle is at 90º .

The second segment:

 • Is a 'Flexible-Polynomial' Motion-Law, from 90 to 360º along the X–axis
 • The Y–axis Value at the end of the second segment is 420º.

This means the Crank rotates

 • from 60º to 420º while the MMA moves from 0 to 90
 • from 120º to 420º while the MMA moves from 90 to 360. Why 60º?

It is the angle of a triangle with the Hypotenuse of 100mm (Radius of Rocker) and an Adjacent of 50mm (Start Position).

Why 120º?

It is the supplementary and obtuse angle of a triangle with the Hypotenuse of 100mm (Radius of Rocker) and an Adjacent of -50mm (End Position). Crank in MechDesigner.

 1 Add a Motion Dimension to a Pin-Joint Part.
 2 Add Linear Motion FB and a Motion FB

Do not connect a wire from the Motion FB to the Motion Dimension FB.

 3 Make the Base Value of the Motion-Dimension 0º.

This Part can be a 'Crank' for a Scotch Yoke Mechanism. 4 Connect the FBs with wires: the Linear Motion FB to the Motion FB to the Motion Dimension FB

At 0º of the Master Machine Angle, the output of the Y–Inverse Sinusoid is 60º.

Hence, the 'Crank' moves to 60º when we 'Home' the Master Machine Angle.

Between 0 and 90 of the MMA:

 • Motion will be: 'Y–Inverse-Sinusoid' motion
 • Angle of movement: from 60º and 120º

Between 90 and 360 of the MMA

 • Motion will be: Flexible-Polynomial motion
 • Angle of movement: rotate from 120º to 420º (60º) This is a schematic of a 'Scotch-Yoke' mechanism.

The End of the Crank has a Pin which engages in a slot. The Slot is vertical in this case, and rigidly attached to a slider that can slide in the horizontal direction.

As the Crank rotates, the Slider moves right to left and then left to right.

While the crank is between 60º and 120º, the Slider moves to the Left with a Constant-Velocity.