An Introduction to the Kinematics of Mechanisms

Stelian Coros

Timeline for the remainder of the course

April 9 14 16 21 23 28 30

No classes

Project one-on-”one” meetings

Last Lecture

Final Project Presentations

Beyond static objects…

• We need models of motion

– We’ve already seen the Finite Element Method

– In principle, can be applied to all types of solid objects -

everything deforms!

– But, computationally very demanding

• Reduced models

– Rigid Bodies

• model for the motion itself (Kinematics)

• model which includes the causes of the motion (Dynamics)

Mechanisms are ubiquitous

Kinematics of Mechanisms

• Kinematics: the study of motion without regard for the

causes of that motion

– No forces, no masses, forget Isaac Newton

• Mechanisms: a system of (rigid) parts working together

The Structure of Mechanisms

The Structure of Mechanisms

Links

Links

The Structure of Mechanisms

Joints

Modeling a Mechanisms

• We describe the configuration of a mechanism using

configuration (or state) variables: s

Modeling a Mechanisms

• As an example: s can be relative joint angles (reduced

coordinates)

Modeling a Mechanisms

• Or s can store full state information (maximal

coordinates)

Types of Links

Types of Joints

Example: Four-bar Linkage

• Constraints vs DOFs

Example: Four-bar Linkage

• Motor controls configuration of entire mechanism

Example: Four-bar Linkage

• Broken mechanism! How do we find a feasible configuration?

= 0 Solve for s s.t.

Mechanism Simulation

Types of constraints

Mechanism Simulation

Mechanism Parameterization and Synthesis

Mechanism Parameterization and Synthesis

Mechanism Parameterization and Synthesis

Mechanism Parameterization and Synthesis

Detecting Singular Configurations

Detecting Singular Configurations

Detecting Singular Configurations

Detecting Singular Configurations

Detecting Singular Configurations

Detecting Singular Configurations

Detecting Singular Configurations

Mechanism Synthesis Example

Assignment 4

• Build a mechanism out of 2D rigid bodies

• Use Rigid Bodies + Constraints

• You’ll 3D print or laser cut your mechanism

Demo

Specifying a scene

Specify Links

Specify Hinge Joints

Specify Tracer Particles

Solving the least squares problem

Distances between

constrained points

Set positions of mechanism

You can build things like this

http://www.youtube.com/watch?v=p__-QbQbntI

Which you could use to build this …

http://www.youtube.com/watch?v=OdnnEZnZNtQ

Timeline for the remainder of the course

April 9 14 16 21 23 28 30

No classes

Project one-on-”one” meetings

Last Lecture

Final Project Presentations