Design the Motion for the Belt.
We need to design the motions a Point on a Chain as it moves around two Pulleys.
The Point moves in an arc as it moves around a pulley.
The Point moves in a straight line as it moves between the pulleys.
Design decisions we have made for the Belt:
•  The belt has twelve (12) pockets 
•  Each pocket and tool has a pitch of 100mm 
Thus, the belt is exactly 12 x 100mm = 1200mm long.
•  Each Pulley has five teeth. 
Hence:
o  Circumference of each Pulley = 500mm, Radius = 500/2π = 79.577mm 
o  Distance between Pulleys = (1200 – 500)/2 = 350mm 
Note: All of the calculations we do in this step can be done much more easily with a:
•  a sketch to define the path of the Belt, 
•  A MotionPath FB will add a MotionPoint to the belt sketch, 
•  a motion can be defined for the MotionPoint. at the inputconnector to the MotionPath FB. 
However, the information below helps us understand the how to edit the Sinusoid Segment.

Background Information: How to model the motion of a Belt and Pulley
The pulleys have equal diameters and their shafts are horizontal with each other. The Pulleys rotate clockwise.
As with motion design, we must find:
2.  The Segment Width of each Segment 
4.  The Segment Parameters and the BlendPoint motionvalues for each segment. 
We must find these for the X and Y Slider Motions of the Piggyback Sliders.
MOTION DESIGN PREPARATION
To prepare the motion for the PiggyBack Sliders, we suggest you follow these steps:

Belt & Pulley Schematic

STEP 1:  Number of Segments 
The number of segments is equal to the number of arc and straight sections of the Belt path.
In the image to the left, you can see there are four segments .
The Number of Segments is the same for the:
•  X and Yaxis Slider motions 

Motion for the XAxis Slider

We will specify that the belt moves at constant velocity. The duration of the motion is 360º.
Then the duration of each segment is proportional to the length of the belt along each straight and arc of the belt path.
Each Segment Width = (Linear Length of Segment / Total Length of Belt) *360.
Each Segment Width = (Number of tool pitches in an arc or straight / Total number of tool pitches along the belt ) *360
Segment Width of Segment & = (2.5/12)=75º
Segment Width of Segment & = (3.5/12)=105º
There are two Segment Types:
: Sinusoid
: Constant Velocity
: Sinusoid
: Constant Velocity

Motion for the YAxis Slider

STEP 4:  Segment Parameters 
Segments &
The Sinusoid Segment Type has three Parameters: Amplitude, Phase, and NumberofCycles.
Amplitude  The Peak of the Sinusoid
•  Amplitude = Peak Value of the Sine Wave. 
•  Amplitude = Radius of Pulley 
•  Amplitude for Segments & = 79.577mm 
The Amplitude is the same for the X and Yaxis Slider motion.
NoofCycles : Number of Sine Waves [No = Number]
One Cycle = One Sine Wave
One Sine Wave = One Full Rotation around a Pulley
Therefore, NoofCycles for Segments & = 180º/360º = 0.5
Phase  The angle, in degrees, at which the Sinusoid Segment starts.
See Below How to Find the Phase Parameter for Sinusoid Segments
The Phase is different for:
•  Segment & 


Segments &
If you enter the correct parameters for the Sinusoid Segments, then MotionDesigner calculates the Position and the Velocity that will match the belt velocity.
You can then select the 'Match' Control Button in the Position and Velocity Controls.
TopTip: To Design the Belt Motion for the Yaxis after the Xaxis (or vice versa)
1.  Prepare the Motion for the Xaxis (or Yaxis): Segment Widths and Segment Types 
2.  Enter the Segment Parameters and the BlendPoint motionvalues 
3.  Save the Active Motion as 'Xaxis Motion' 
4.  Use the 'Reopen and Append' option to reopen the 'Xaxis Motion'. 
The new motion in the new motion tab is identical to the 'Xaxis Motion'.
5.  Rename it to 'Yaxis Motion' 
You only need to edit one parameter  the Phase of each Sinusoid Segment  to design the Yaxis motion.


We need to find and enter the Phase Parameter four times. We have two motions, each with two sinusoid segments:
1.  Xaxis motion, Segment 
2.  Yaxis motion, Segment 
3.  Xaxis motion, Segment 
4.  Yaxis motion, Segment 
To find the phase for each, it is best to draw a sketch to visualize the motion  position and velocity  of the point on a belt as it starts, then moves around each pulley and arc, and finally exits the pulley to move along a straight section of the belt path.
Remember, we have already entered the Amplitude and the Number of Cycles parameters.


Segment  Righthand Pulley
Xaxis motionvalues
Position: A : X= 0mm, B : X increases to 79.577mm (peak X value), C : decreases to 0mm.
Velocity: A : Vx = Max in + X direction, B : Vx = 0mm/s, C : Vx = Max in – X direction
Y Values:
Position: A : Y= 79.577mm (peak X value), B : Y decreases to 0mm, C : decreases to 79.577mm.
Velocity: A : Vy = 0mm/s, B : Vy = Max in – Y direction , C : Vy = 0mm/s


Xaxis Phase: Segment
You can see that the part of the sinewave from 0º to 180º agrees with the motion of the point in the Xaxis direction as it moves around the righthand pulley, from A to C
Therefore, the Phase of the Xaxis Motion for the first Sinusoid Segment = 0

Sinusoid Segment Parameters: Segment 1, XAxis Slider Motion


Yaxis Phase: Segment
You can see that the part of the sinewave from 90º to 270º agrees with the motion of the point in the Yaxis direction as it moves around the righthand pulley from A to C
Therefore, the Phase of the Yaxis Motion for the Sinusoid Segment = 90

Sinusoid Segment Parameters: Segment 1, YAxis Slider Motion


Segment  Lefthand Pulley
X Values:
Position: A : X= 0mm; B : X decreases to 79.577mm (peak X value); C : increases to 0mm.
Velocity: A : Vx = Max in X direction, B : Vx = 0mm/s, C : Vx = Max in +X direction
Y Values:
Position: A : Y= 79.577mm; B : Y increases to 0mm; C : increases to 79.577mm.
Velocity: A : Vy = 0mm/s; B : Vy = Max in +Y direction; C : Vy = 0mm/s


Xaxis Phase:
You can see that the part of the sinewave from 180º to 360º agrees with the motion of the point as it moves around the lefthand pulley.
Therefore, the Phase of the Xaxis Motion for the Sinusoid Segment = 180


Yaxis Phase:
You can see that the part of the sinewave from 270º to 90º (360+90) agrees with the motion of the point as it moves around the lefthand pulley.
Therefore, the Phase of the Yaxis Motion for the Sinusoid Segment = 270

Complete the Model in MechDesigner

STEP 1:  Add two Motion FBs and one LinearMotion FB to the graphicarea. 
STEP 2:  Edit a Motion FB and select the X motion in the dropdown box 
STEP 3:  Edit the other Motion FB and select the Y motion in the dropdown box 
STEP 4:  Connect the LinearMotion FB to both Motion FBs 
STEP 5:  Connect the Motion FB linked to the X Motion to the Horizontal, XSlider 
STEP 6:  Connect the Motion FB linked to the Y motion to the Vertical, YSlider 
STEP 7:  Add a TracePoint to a Point on the YSlider 
STEP 8:  Cycle the Kinematicchain 
The TracePoint shows the path of the Belt.


This is the KinematicsTree for the Piggyback Sliders.
Notice that there is:
