<< Click to Display Table of Contents >> Navigation: Getting Started Tutorials  MechDesigner > Tutorial 15: Patterns  IndexingChain example > Step 15.1: Piggyback Sliders and the Belt Motion 
NOTE:
Tutorial 15 was written before the MotionPath FB was available.
Piggyback Sliders are included, below. They remain an important modeling technique.
What is a Piggyback? I am not sure if it is only an English term?
When someone is off the ground and on the back of a standing person, and their hands are around the standing person's neck (to hold, not to strangle!) and their legs around each side and held by the standing person's arms, then the person that is off the ground is being given a Piggyback.
The person on the back (imagine he can climb a ladder that is also held by the person on the ground!) has a motion that is combination of their own motion and the motion of the person on the ground.
Why Piggyback Sliders?
We can design Parametric Motions  that is, a motion for the person moving on the ground, (parallel to the Xaxis,) and a motion for the person being given the Piggyback, (parallel to the Yaxis). The result is a XY Planar motion that we can easily design.
Why not Piggyback Rockers?
Yes, we can have Piggyback Rockers also  exactly like a SCARA robot.
However, it is almost impossible to design the motions for Piggyback Rockers and predict the planar motion of the Point at the end of the SCARA robot.
We add two MotionParts  Sliders  and assemble them as Piggyback Sliders.
We will name the Sliders : SliderX and SliderY
In this tutorial, we design motions for the SliderX and SliderY such that a Point on the SliderY follows the path of a Point on a belt. We motions for SliderX and SliderY are designed here.
Quick Instructions:

Add the XSlider


Edit the XSlider, Add a Vertical Line


Add the 'Y'Slider


Get Motions for the Sliders  Example Motions


Run menu > Cycle (or ALT+C) X Motion This is a motion for the Xaxis. Use a Motion FB to link this motion to the MotionDimension FB to move the XSlider. 

Y Motion This is a motion for the Yaxis. Use a different Motion FB to link to the MotionDimension FB to move the YSlider. These two example motions define the motion along the XYpath on the MechanismPlane We show the XYpath in the graphicarea with a TracePoint. 
Design the Motion for the Belt.
We need to design the motions an imaginary point on a Belt as it moves around two Pulleys.
The Point moves in along an arc as it moves around the pulleys.
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
•Each Pulley has five teeth
oThe beltlength is exactly 12 × 100mm = 1200mm.
oCircumference of each Pulley = 5 × 100 = 500mm,
oRadius of each Pulley = 500/2π = 79.577mm
oDistance between Pulleys = (1200 – 500) ÷ 2 = 350mm
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: STEP 1: The number of segments STEP 2: The Segment Width of each Segment STEP 3: The Segment Types STEP 4: The Segment Parameters and motionvalues for each BlendPoint. We must do 14 for SliderX and SliderY. 

Schematic  Belt and two Pulleys 
STEP 1:NumberofSegments 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 SliderX and SliderY 

STEP 2:Segment Width 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 = (Linearize Length of Segment / Total Length of Belt)×360. Or, remember that the belt has 12 pockets, and the pitch of each pocket is 100mm. Therefore: Each Segment Width = (Number of Pockets (on the Arc or Linear section of the Belt) / Total number of Pockets along the belt ) × 360 Segment Width of Segment & = (2.5÷12)×360=75º Segment Width of Segment & = (3.5÷/12)×360=105º 

STEP 3:Segment Type There are two Segment Types: : Sinusoid : Constant Velocity : Sinusoid : Constant Velocity STEP 4:Segment Parameters Segments & The Sinusoid Segment Type has three parameters: Amplitude, Phase, and NumberofCycles.


Sinuoid MotionLaw  SegmentParameters: Xaxis motion 

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.

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 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 A sinewave from 0º to 180º agrees with the horizontal motion of the Xaxis Slider as it moves around the righthand pulley, from A to C Therefore, the Phase of the Xaxis Motion for the first Sinusoid Segment = 0 

Yaxis Phase: Segment A sinewave from 90º to 270º agrees with the vertical motion of the Yaxis Slider as it moves around the righthand pulley from A to C Therefore, the Phase of the Yaxis Motion for the Sinusoid Segment = 90 

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: A sinewave from 180º to 360º agrees with the horizontal motion of the Xaxis Slider as it moves around the lefthand pulley. Therefore, the Phase of the Xaxis Motion for the Sinusoid Segment = 180 

Yaxis Phase: A sinewave from 270º to 90º (360+90) agrees with the vertical motion of the Yaxis Slider as it moves around the lefthand pulley. Therefore, the Phase of the Yaxis Motion for the Sinusoid Segment = 270 
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. 