﻿ Y-Inverse-Sinusoid [Special]

# Motion-Law: Y–Inverse-Sinusoid

### Y–Inverse-Sinusoid

Note: We recommend that you use the Constant-Velocity Inverse Crank,

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 'Y–Inverse Sinusoid' 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.

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

If EP > SP, then the Constant-Velocity motion is from left to right, not right to left

Segment Parameters.

Amplitude: R [Example is 100]

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

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

 This does not need to equal the actual length of the Rocker. It can easily be equal to 100. It it easier to understand the parameters when Amplitude = 100.

Start Position [Example is +50]

Start Position must be within the maximum range as specified by the 'Rocker Radius' parameter ±100% × Rocker [practically less than this]

Specifies the motion value, in linear units, that the tip of the part is at when it starts to move at a Constant-Velocity.

End Position [-R ≤ End Position ≤ R] [Example is -50]

End Position must be within the maximum range as specified by the 'Rocker Radius' parameter ±100% × Rocker [practically less than this]

Specifies the motion value, in linear units, that the tip of the part is at when it ends tits move at a Constant-Velocity.

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

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

The example motion, with two segments.

Segment 1:

 • It is 90º of the X-axis
 • 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 becomes +60º†, when the Master Machine Angle (MMA) is 0º .
 o The Segment Y–axis Value becomes +120º‡ when the Master Machine Angle is at 90º .

Segment 2:

 • It is 270º if the X-axis
 • 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 120º while the MMA moves from 0 to 120
 • from 120º to 420º while the MMA moves from 90 to 360.

NOTE:

The motion is most typically applied to rotating Parts - that is Cranks or Rockers.

However, it can be used to control the motion of any Part for any reason - just like any other motion.

† 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 rotating-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 FB = 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.

Tutorials and Reference Help Files for MechDesigner and MotionDesigner 14.2 + © Machine, Cam, Mechanism, and Motion Design Software by PSMotion Ltd