Collection of Results for the Computer Aided Design of Mechanisms

Mathematica Notebooks for Linkage Design

Planar Linkages
4R Linkage Classification: This notebook plots and classifies a planar 4R linkage.

4R Linkage Analysis: This notebook calculates and plots the joint angle values of a planar 4R linkage

4R Linkage Animation: This notebook analyses and animates a planar 4R linkage.

4R Linkage Design: This notebook formulates and solves the design equations for a planar 4R linkage.
The following is a coordinated set of notebooks for three-position synthesis:
  • ThreePosDesign: This takes three positions as input and formulates and solves the design equations
  • ThreePosCheck: This checks that each of the design positions is on the same solution mode
  • ThreePosAnimation: This generates an animation in Mathematics of the linkage
  • ThreePosPOV: This generates an "include" file for POV-Ray that allows rendering of the animation
  • FourBarScale.pov: This is the POV-Ray file that generates the rendering
Select here to see the animation generated by this set of files. Thanks are due to Haijun Su for developing the macros for this animation.

Spherical Linkages
SphereVertex.nb--This notebook assists in specifying the joint axis vectors that define a spherical 4R linkage .

SphereAnalysis.nb--This notebook analyzes a spherical linkage given the set of unit vectors defining its joint axes.

SphereAnimate.nb--This notebook generates an animation of the spherical 4R linkage.
Select here for a full-sized version of this figure.

Select here for a a QuickTime animation (7 MB).
These notebooks provide three-orientation synthesis of spherical 4R linkages:
  • Sphere3PosDesign: This takes three orientations as input and formulates and solves the design equations.
  • Sphere3PosCheck: This checks that each of the design orientations is on the same solution mode.
  • Sphere3PosAnimation: This generates an animation in Mathematics of the linkage.
  • Sphere3PosPOV: This generates an "include" file for POV-Ray that allows rendering of the animation.
  • SpFourBarAnimate.pov: This is the POV-Ray file that generates the rendering.

Graphics Generated by Students
Select here to see Terrence Yao's animation of a Chebychev linkage.
Select here to see Terrence Yao's animation of his two position synthesis of this 4R linkage.
More animations by Terrence Yao:

Select here (or the image above left) to download an .avi file (2.6MB) of the three position synthesis of a planar linkage.

Select here (or the image above right) to download an .avi file (2MB) of a spherical linkage.
A Feeding Mechanism based on a Spherical Linkage

The movement of a spherical linkage allows the feeding mechanism to be off to the side of the client while the spoon selects and delivers food. Thus it avoids obstructing the view and social interaction of the individual.

Select here to download the .avi design and animation (2.3MB) prepared by Terrance Yao.

Student Concepts for New Products using Spherical Linkages
Budiarto The: Car Side Mirror Linkage (1.7 MB) Ryan Kelly: Prosthetic Thumb Linkage (1.1 MB) Terrence Yao: Car Seat Assist Linkage. The first animation shows the linkage in a car (7.4 MB). The second focuses on the performance of the linkage (2.4 MB).
In Mo Yeo: Pitching Linkage (0.8 MB)
Jeremy Kim: Lamborgini Door Linkage (0.5 MB). Note the car is rotated 45 degree downward, so the door is actually opening vertically. Tyler Reid: Support Linkage for Night Vision Goggles (2.7 MB).

Spatial Linkages

Spatial RR Synthesis: This notebook develops the design equations for three position synthesis of spatial RR robots. The centerpiece is the symbolic elimination from four non-linear equations in four unknowns to a single cubic equation. Along the way, we develop and use operations for line geometry, including determining the principal axes of a cylindroid. This is described in the paper:
Select here for an animation (2.1MB) of a Bennett Linkage (Tsai and Roth 1973).
Select here for a more detailed animation (5.2MB).
Visitors since November 1, 2000