﻿ Two Degrees-of-Freedom Planar Kinematic-Chains

# Tutorial 11: Two Degrees-of-Freedom Planar Kinematic-Chains

## Two Degree of Freedom Planar Kinematic-Chains

Background: Properties of a Point that moves along an XY-Path

If a Point has a general motion on the Mechanism-Plane, we can think of its:

 A. Path on the Plane, or, 'Where it moves on the Plane'.
 B. Motion along the Path, or, 'How it moves along the Path'.

In MechDesigner, to define the motion for a Point on the Mechanism-Plane, you can use:

 1 Piggyback Sliders : Slider(A), to which we add Slider(B) that moves at right-angles to Slider(A). Design two motions: a motion for Slider(A) and Slider(B).
 2 Motion-Path FB : sketch the Path for the Point. Design one motion for a Point along the Path.

Some designs are easier to design with Piggyback Sliders and others with a Motion-Path FB.

This tutorial uses Piggyback Sliders.

 An example of a Piggyback slider application: A tool (say a vacuum cup) must take a carton from a stationary magazine and insert it into a pocket on a moving conveyor. To place the carton, you must move the tool along with the moving conveyor (say, the X-direction) and also move it down into the pocket (say, the Y-direction) at the same time. To make sure the carton does not touch the sides of the pocket, we must synchronize the motion of the tool in both the X and Y directions. This design problem is easier to solve with Piggyback Sliders.

## Two Degree-of-Freedom Kinematic-Chains

 ➢ Step 11.1: Introduce the Piggyback Sliders
 ➢ Step 11.3: Remove the XY Piggyback Sliders

#### Robots: XY-Path to give the letters 'MD'

2D Point Motion

Machines that move a point in the X- and Y-axis directions, include:

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

Each machine is a two degree-of-freedom (2 DOF) system.

Many kinematic-chains have two degrees-of-freedoms.

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

 This SCARA robot, as another 'Plotter', is also a two degree-of-freedom system. The two inputs rotate The motions we give to the two motors are not the same as those we give to sliders in the Gantry Robot. in fact they are much more complex. Their movements are solved with Inverse-Kinematics.
 This SCARA robot, as another 'Plotter', is also a two degree-of-freedom system. The two inputs rotate The motions we give to the two motors are not the same as those we give to sliders in the Gantry Robot. in fact they are much more complex. Their movements are solved with Inverse-Kinematics.

 Here is a different 'Plotter'. An example is shown here, https://www.youtube.com/watch?v=b2UkmcPLEOs In this model, the motors are attached to the frame. It is potentially a much faster (more responsive, more accurate) system, because the one motor does not need to move the mass of the other motor.

2D Planar, Curvilinear Motion

A Plane that is coplanar with a fixed-plane has 3 degrees-of-freedom.

However, if each Point on the Plane has the same general XY-motion - that is, the Plane moves, but does not rotate relative to the fixed-plane - then it has Curvilinear Motion.

Planar Guidance Click to Play Video

In this model:

 • we have fixed three 'motors', shown as black cylinders, to 'Ground'.
 • we have connected a Part (a Dark Green colour) to each motor.
 • we keep the tool platform at the same angle relative to the frame while the other two axes write the letters 'MD'.
 • This can be used with DNA sequencing where multiple pipettes need to take sample or add an 'ingredient'.

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