﻿ Getting Started Tutorials - MechDesigner > Tutorial 11: Two Degrees-of-Freedom Planar Kinematic-Chains > Step 11.1: Piggyback Sliders as XY Table

# Step 11.1: Piggyback Sliders as XY Table

### About Piggyback Sliders

 The Piggyback Slider configuration is two Sliders: •Slider(A) : moves along the X-axis† of the Mechanism-Plane •Slider(B) : moves relative to Slider(A), and parallel to the Y-axis† of Slider(A) The Piggyback Slider Configuration is only one way to model an XY-Path.   You can also use a Motion-Path FB. † The Sliders do not need to be in the X-axis and Y-axis directions or even at right-angles to each other. We describe them in these directions for convenience only. They can equally be in the Radial and Tangential directions of a circle.

### Mechanical Systems that follow an XY Motion-Path:

Piggyback Sliders, and a Drive

 •Piggyback Sliders •The motion of each Slider has a linear relationship to the motion of the motor. •Each motor to rotate a Pulley to move a Belt, or a motor to rotate a Ball-Screw to move a Nut.

Piggyback Sliders and a Dyad and a Drive.

 •Piggyback Sliders •Connect dyads from the machine-frame to each Slider. •Add Cams or Servomotors to drive a Part in each dyad •Inverse-kinematics to calculate the motions for the cam-followers or servomotors to give the motions designed for the XY-Table- See Step 11.2

Translating Beam (a Part that moves on the Mechanism-Plane but does not rotate)

 •Piggyback Sliders to define the XY-Motion •Design a mechanism with a translating-beam that is not physically connected to the machine-frame. •Look at this video.

Terminology:

 Rectilinear Translation: All points in a Part have the same translating and parallel motions. Curvilinear Translation: All points in a Part have the same, but not necessarily straight, motions.

### Add Piggyback Sliders - Quick Instructions

Quick Instructions:

 1.Add the X-Slider to a horizontal Line in the Base-Part 2.Edit the X-Slider. Add a Line that is parallel to the Y-axis 3.Add the Y-Slider to the Line that is parallel to the Y-axis of X-Slider. 4.Design the motions for each Slider. 5.Add a Trace-Point to a Point that moves with the Y-Slider. 6.Run menu  > Cycle to watch the Piggyback Sliders.

### Add Piggyback Sliders - More Detailed Instructions

 1.Edit the Base-Part 2.Part-Editor: Geometry toolbar > Add Line , Constraints toolbar > Add Horizontal : Click the Line; Close the Part-Editor 3.Mechanism-Editor: Add a Part; Add a Slide-Joint between the Part and the Line in the Base-Part 4.Mechanism-Editor: Add a Motion-Dimension FB to identify the X Slider 5.Mechanism-Editor: Add a Linear-Motion FB and a Motion FB to the graphic-area Connect the FBs with wires. 6.Rename the Slider to X SLIDER

Edit the X-Slider, Add a Vertical Line

 1.Mechanism-Editor: Edit X-Slider Part : Part-Editor:  Edit length to 100mm. 2.Part-Editor: Geometry toolbar > Add Line , Drag UPWARDS to add the Line : Constraints toolbar > Add Vertical click the Line; 3.Part-Editor: Geometry toolbar > Add Dimension :Line = 100mm 4.Part-Editor: Constraints toolbar > Coincident , Click start-Point of the two Lines . 5.Close the Part-Editor

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

Get Motions for the Sliders

 1.Mechanism-Editor: Edit the Motion FB connected to the X-Slider to open the Motion FB dialog-box 2.Mechanism-Editor: Select X-Motion in the drop-down box. 3.Close the Motion FB dialog-box 4.Mechanism-Editor: Edit the Motion FB connected to the Y-Slider to open the Motion FB dialog-box 5.Mechanism-Editor: Select the Y-Motion in the drop-down box for the Y-Slider 6.Close the Motion FB dialog-box Show the Trace-Path: 7.Mechanism-Editor: Do Kinematic-element > Add Trace-Point , click a Point on the Y-Slider

Run menu > Cycle (or ALT+C)

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 the motion along the XY-path on the Mechanism-Plane

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

### Degrees-of-Freedom of Piggyback Sliders

 Degrees-of-Freedom and Mobility of Piggyback Sliders Gruebler Equation to find the number of Degrees-of-Freedom (F): F = 3(P-1) – 2J  : P = Number of Parts (1 × Base-Part + 2 × Added-Parts) ; J = Number of Joints ( 2 × Slide-Joints) F = 3×(3-1) – 2×2 F = 6 – 4 = 2 Mobility = # Degrees-of-Freedom(F) – # Motion-Dimensions = 2 – 2 = 0.

### Kinematics Tree of Piggyback Sliders

 Kinematics-Tree for Piggyback Sliders. 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

 An XY-Gantry Robot Look at the video to the left. This 'Plotter' moves a Pen along a slide, say the Y-axis slide. The X-axis carries the Y-axis slide.  The combined movement plots the drawing. With this machine, there is an EXACT linear-equivalence between the XY-Path and the control positions of the slider motors. The system is Kinematically Linear. This 'Plotter' moves a Pen with a slider along the X-axis. A different slider carries the X-axis slider, but along the Y-axis. The two movements of the slider plot the drawing.