Getting Started Tutorials - MechDesigner > Tutorial 11: Two Degrees-of-Freedom Planar Kinematic-Chains

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. See: Motion-Path and Blend-Curves.

† 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

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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

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Add the X-Slider

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

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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

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Add the 'Y'-Slider

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

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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

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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.

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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

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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

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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.

Step 11.1: Piggyback Sliders as XY Table