# Interactive Type Synthesis of Mechanisms

### Eric Enderton

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-90-570

March 1990

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1990/CSD-90-570.pdf

As a step towards CAD systems that model function as well as form, we have developed an interactive tool for qualitative mechanism design. Called the mechanism editor, it enables the user to quickly sketch abstract planar mechanisms made up of polygonal links connected by revolute and prismatic joints. The user may interactively control the parameter of a joint, and the editor will compute and display the resulting motion of the entire mechanism.

When the user requests an animation, the editor builds a plan to be executed repeatedly as the user flexes the input joint. The graph of the mechanism's topology, in which each link is represented by a node and each joint by an edge, is used for counting degrees of freedom, including the detection of overconstrained submechanisms. The graph is modified during the planning stage to represent the portion of the mechanism that remains to be solved. Each step in the plan solves a small subgraph that matches the graph of one of the available base cases. This step computes the relative positions of the links in the subgraph. This subgraph is then contracted to a single node, leaving a smaller graph to be solved. After a number of steps, the graph is reduced to one node, and the positions of every link are known relative to ground. There are some mechanisms whose graphs cannot be solved in this fashion.

A set of base cases, composed of the RRR, PRR, and RPR mechanisms, is described in detail. Simple trigonometry yields closed-form solutions for these base cases. Therefore the whole plan represents a closed-form solution. Each base case typically has either two possible solutions, in which case the plan step must choose one of them, or it has zero solutions, in which case the mechanism breaks. A number of possible policies for these situations are presented.

Several earlier systems, most of them descendants of Sutherland's Sketchpad, are described and compared to the mechanism editor. Some implementation details are presented, including control structures for the user interface and for the planner.

BibTeX citation:

@techreport{Enderton:CSD-90-570, Author = {Enderton, Eric}, Title = {Interactive Type Synthesis of Mechanisms}, Institution = {EECS Department, University of California, Berkeley}, Year = {1990}, Month = {Mar}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1990/5577.html}, Number = {UCB/CSD-90-570}, Abstract = {As a step towards CAD systems that model function as well as form, we have developed an interactive tool for qualitative mechanism design. Called the mechanism editor, it enables the user to quickly sketch abstract planar mechanisms made up of polygonal links connected by revolute and prismatic joints. The user may interactively control the parameter of a joint, and the editor will compute and display the resulting motion of the entire mechanism. <p>When the user requests an animation, the editor builds a plan to be executed repeatedly as the user flexes the input joint. The graph of the mechanism's topology, in which each link is represented by a node and each joint by an edge, is used for counting degrees of freedom, including the detection of overconstrained submechanisms. The graph is modified during the planning stage to represent the portion of the mechanism that remains to be solved. Each step in the plan solves a small subgraph that matches the graph of one of the available base cases. This step computes the relative positions of the links in the subgraph. This subgraph is then contracted to a single node, leaving a smaller graph to be solved. After a number of steps, the graph is reduced to one node, and the positions of every link are known relative to ground. There are some mechanisms whose graphs cannot be solved in this fashion. <p>A set of base cases, composed of the RRR, PRR, and RPR mechanisms, is described in detail. Simple trigonometry yields closed-form solutions for these base cases. Therefore the whole plan represents a closed-form solution. Each base case typically has either two possible solutions, in which case the plan step must choose one of them, or it has zero solutions, in which case the mechanism breaks. A number of possible policies for these situations are presented. <p>Several earlier systems, most of them descendants of Sutherland's Sketchpad, are described and compared to the mechanism editor. Some implementation details are presented, including control structures for the user interface and for the planner.} }

EndNote citation:

%0 Report %A Enderton, Eric %T Interactive Type Synthesis of Mechanisms %I EECS Department, University of California, Berkeley %D 1990 %@ UCB/CSD-90-570 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1990/5577.html %F Enderton:CSD-90-570