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:
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. For the motiondesign, we need to calculate:
We must find these for the X and Y Slider Motions of the Piggyback Sliders. MOTION DESIGN PREPARATIONTo prepare the motion for the PiggyBack Sliders, we suggest you follow these steps: 

Belt & Pulley Schematic 
The numberofsegments 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 NumberofSegments is the same for the:


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 of the 4 segments is proportional to the length of the belt along each of the 4 segments that define the 2 × linear and 2 × arcs of the belt path. Each Segment Width = (Lineariz Length of Segment / Total Length of Belt)×360. Each Segment Width = (Number of Tool/Link Pitches on Arc or Linear section / Total number of tool pitches along the belt )×360 Segment Width of Segment & = (2.5÷12)×360=75º Segment Width of Segment & = (3.5÷/12)×360=105º
There are two Segment Types: : Sinusoid : Constant Velocity : Sinusoid : Constant Velocity 

Motion for the YAxis Slider 
Segments & The Sinusoid Segment Type has three parameters: Amplitude, Phase, and NumberofCycles.


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 for the Position and Velocity Controls.

How to Find the Phase Parameter for the Sinusoid Segments
We need to find and enter the Phase Parameter four times. We have two motions, each with two sinusoid segments:
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 Yaxis motionvalues: 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 phase 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 phase 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
The TracePoint shows the path of the Belt. 

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