Linkage Animations:

Planar, Spherical and Spatial 4R Chains


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Mechanical Design 101

Animations

Planar, Spherical and Spatial Four-bars

Concepts for new products

Notebooks for analysis and design

Kinematic Synthesis of Planar, Spherical and Spatial Linkages

Recent results in the design of 4R closed chains use the "configuration manifold" of the movement of the coupler link to guide the selection of task positions, such that they are consistent with smooth movement of the linkage. This manifold is also known as the "image curve" of the linkage.

Linkage Synthesis with Velocity Specifications

The animation illustrates a planar 4R linkage that was designed using three planar positions and two velocity specifications. The configuration manifold, or image curve, of the linkage was used to pick velocity specifications that resulted in smooth movement of the linkage.


Linkage Animations

This animation shows three position synthesis of a planar 4R linkage. The animation is generated using POV-ray. (HaiJun Su)
This animation shows three position synthesis of a spherical 4R linkage. POV-ray was used to generate the animation. (HaiJun Su)
This is a POV-ray animation of the spatial four-bar linkage called the Bennett Linkage. (HaiJun Su)
Select here to see an animation of a Chebychev linkage. (Terrance Yao)
Select here to see an animation of this cover mechanism. (Terrance Yao)
This is a planar linkage designed to pass through three positions and over an obstacle. Terrance Yao animated this using Visual Nastran.
This is a spherical four-bar llinkage animated by Terrance Yao using Visual Nastran.
A Spherical Linkage Feeding Machine

The spherical linkage allows the feeding mechanism to be off to the side of the client while the spoon delivers food. It avoids obstructing vision and social interaction.

Terrance Yao animated this design using Visual Nastran.

Student Concepts for New Products using Spherical Linkages

(select the image to load the animation)

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).

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.

These notebooks provide planar 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

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.

The notebooks provide three-orientation synthesis.

  • 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.


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