﻿ Step 11.1: Piggyback Sliders as XY Table

# Step 11.1: Piggyback Sliders as XY Table

The Piggyback Slider configuration is a:

 • Slider[A], that moves along the X-axis† of the Mechanism-Plane
 • Slider[B] mounted to Slider[A], and moves along the Y-axis† of the Slider[A]

The 'Piggyback Slider' configuration is only one way to model an XY-Path. See Motion-Path and Blend-Curves.

The Sliders are not always in the X and Y-axis directions. For example, they may be in the Radial and Tangential direction relative to radius line of a circle. However, here, it is convenient to label the Sliders as X & Y.

#### Mechanical Systems that follow the 'XY'-Path:

 • Linear Slides
 o The Piggyback Sliders are modelled in the same way as the Linear-Motion Technology' [the motors and the mechanics].
 o The motors that drive the 'Sliders' have the same nominal* motion as the Piggyback Sliders. See Step 11.1

* For example, a motor may rotate a Pulley to move a Belt, or a motor may rotate a Ball-Screw to move a Nut. In each case, the motors may rotate a different number of rotations, but their rotation is a linear relationship to the Slider's motion.

 a. Use linear-slides to design an XY-table.
 b. Connect Dyads between the linear-slides and the Machine Frame.
 c. Use Cams or servomotors on the Machine Frame to drive the Dyads and thus the XY-table

Design and add motions to the XY-table directly. Given the motion of the XY-table, MechDesigner will use inverse-kinematics to calculate the motions for the Cam-Followers or servomotors. See Step 11.2

 • A 'Translating Beam'
 o It is possible to configure Parts and Joints to move a translating beam in the X and Y directions where you do not need to use linear-slides.
 o Look at this video of the 5-bar Planar Guidance Robot. It is an example that can give general X,Y and Rotation.
 o Use Piggyback Sliders in the MechDesigner model to specify the XY-Path, even though they are not in the mechanical system. See Step 11.3.

Technical Note:

Translation: all points in the body move along parallel paths, have the same velocity and acceleration, keep the same orientation and the body does not rotate

 • Rectilinear Translation: Translation + all points move along a straight line.
 • Curvilinear Translation: Translation + general motion of a rigid body (same as Translation)

### Quick Instructions: Add Piggyback Sliders

Quick Instructions:

 1 Add a Part that is the X-Slider to a horizontal Line.
 2 Edit the X-Slider. Add a Line that is perpendicular[⊥] to the CAD-Line. Close the Part-Editor.
 3 Add the Part that is the Y-Slider to the new Line in the X-Slider
 4 Design the motions for each Slider
 5 Add a Trace-Point to a Point that moves with the Y-Slider.
 6 Cycle the Mechanism to watch the kinematic-chain move.

### 'Detailed Instructions: Add Piggyback Sliders'

 STEP 1: Edit the Base-Part; Add a Horizontal Line; Close the Part-Editor
 STEP 2: Add a Part; Add a Slide-Joint between the Part and the Line in the Base-Part
 STEP 3: Add a Motion-Dimension FB to identify the X Slider
 STEP 4: Add a Linear-Motion FB and a Motion FB to the graphic-area
 STEP 5: Connect the FBs
 STEP 6: Rename the Slider Part to 'X SLIDER'

Edit the X-Slider, Add a Vertical Line

 STEP 1: Edit the length of the X-Slider Part

I have changed it to 100mm.

 STEP 3: Add a Vertical Constraint to the Line
 STEP 4: Dimension and add Constraints to fully specify the Line

The length of the new Line is 100mm. The Origin of the new Line is 'Coincident' with the Origin of the Part.

 STEP 5: Close the Part-Editor

 STEP 1: Add a Part; Add a Slide-Joint between the new Part and the vertical Line in the X-Slider
 STEP 2: Add a Motion-Dimension FB to specify the Position of the Y-Slider.
 STEP 3: Add a Linear-Motion FB and a Motion FB to the graphic-area
 STEP 4: Connect the FBs
 STEP 5: Rename the new Slider Part to 'Y-SLIDER'

Get Motions for the Sliders

 STEP 1: Double-click the Motion FB connected to the X-Slider
 STEP 2: Click the Motion for the X-Slider
 STEP 3: Double-click the Motion FB connected to the Y-Slider
 STEP 4: Click the Motion for the Y-Slider

Show the Path traced out by the Y-Slider

 STEP 5: Use Add Trace-Point in the Mechanism Local toolbar to add a Trace-Point to a Point in the Y-Slider

 STEP 6: Run menu > Cycle, [or use ALT + C, [C for R13+]]

X Motion

This is a Motion for the X-axis.

Use a Motion FB to link this motion to the Motion-Dimension FB to move the X-Slider.

Y Motion

This is a Motion for the Y-axis.

Use a different Motion FB to link to the Motion-Dimension FB to move the Y-Slider.

These two example motions define an XY motion path on the Mechanism-Plane

We can show the XY motion path in the graphic-area with a Trace-Point.

### Degrees-of-Freedom of Piggyback Sliders

'Degrees-of-Freedom' and 'Mobility' of Piggyback Sliders

The Piggyback Slider kinematic-chain has:

 • two 'added Parts' (with the BasePart, there are three Parts in total)
 • two Joints.

Gruebler Equation to find the number of Degrees-of-Freedom (F):

F = 3(P-1) - 2J  : P = Number of Parts ; J = Number of Joints

F = 3*(3-1) - 2*2

F = 6 - 4 = 2

Mobility = # Degrees-of-Freedom - # Motion-Dimensions = 2 - 2 = 0.

### Kinematics Tree of Piggyback Sliders

This is the Kinematics-Tree for 'Piggyback Sliders'.

Note: there is:

 • One kinematic-chain [Solved Mechanisms]

The Solved Mechanism has:

 • Two Sliders

### Machines that use Piggyback Sliders

Example machines include:

 • Pen Plotters
 • Water-Jet Cutters
 • Laser Markers or Cutters

The tool is equivalent to a 'Point'.

An XY 'Gantry' Robot

Imagine a 'Pen Plotter'. Look at the video to the left.

This 'Plotter' moves a Pen along a slide, say the X-axis slide. The Y-axis carries the X-axis slide.  The combined movement plots the drawing.

With this machine, there is an EXACT link between a Point at position X1,Y1 and the control positions of the slider motors. The system is Kinematically Linear.

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