Special Topics in Computer Science Computational Modeling for SnakeBased Robots Introduction to Asse

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Special Topics in Computer ScienceComputational
Modeling for Snake-Based RobotsIntroduction to
Assembly ModelingWeek 2, Lecture 1

• William Regli
• Geometric and Intelligent Computing Laboratory
• Department of Computer Science
• Drexel University
• http//gicl.cs.drexel.edu

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Building Multidisciplinary Model

• Class Goal create multidisciplinary engineering
  models
• Challenge Learn enough about each discipline to
  create integrated models!
• Last week modeling parts
• Today putting parts together!
• i.e. creating assemblies

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Where we stand

• You have a physical design you prototyped with
  Legos
• You have your individual 3D models for the
  elements of the design
• How to put them together?

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Transformations to Change Coordinate Systems

• Issue the world has many different relative
  frames of reference
• How do we transform among them?
• Example CAD Assemblies Animation Models

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Example A Scanner Head Assembly
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Goal of Assembly Modeling

• Products are rarely individual parts
• Typically, products are designed top down as
  assembly models
• For this class, we are interested in the data
  structures for assemblies

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Assembly Modeling

• Parts can be defined with mating features on
  them.
• Features can be mated directly.
• An assembly database builds up automatically.
• Assembly knowledge can be accessed.

• Information in assembly models
• What parts mate to what parts
• What features define the mates and where they are
  on the parts
• What interfaces must be controlled, plus a formal
  way of describing them
• Constraints and rule-checking
• about assembly in the small
• about assembly intent in terms of features
• about assembly in the large, including alternate
  parts
• It is a completely abstract and general model
  based on connectivity
• Geometry is an attribute of the parts

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Degrees of Freedom

• An objects location in space is completely
  specified when three translations (X, Y, Z) and
  three rotations ( ) are specified
• How many DOFs are constrained?
• cube on table (x-y plane)
• cube at floor-wall interface
• cube at floor-two walls interface
• ball on table
• ball at floor-wall interface
• round peg in blind round hole

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Constraints

• Proper constraints provide a single value for
  each of a bodys 6 degrees of freedom
• This is done by establishing surface contacts
  with surfaces on another part or parts
• If less than 6 dof have definite values, the body
  is under-constrained
• If an attempt is made to provide 2 or more values
  for a dof, then the body is over-constrained
  because rigid bodies have only 6 dof

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Constraints (examples)
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Constraints (examples)
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Creating an Assembly

• Parts join at places called assembly features
• Different features constrain different numbers
  and kinds of degrees of freedom of the respective
  parts (symmetrically)
• Parts may join by
• one pair of features
• multiple features
• several parts working together, each with its own
  features
• When parts mate to fixtures, dofs are constrained

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Assembly Features

• Examples
• Fixed
• Revolute
• Planar
• Screw
• Spherical
• Prismatic

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Example Phillips screw
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Example Feature
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Relating Features to Assembly Models
Depends on parts
Does not depend on parts
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Data Structures for Assemblies

• Typically an attributed graph or tree
• Vertices parts
• Edges
• Part-to-part contacts
• Usually represented as joints
• Attributes
• Kinematic specifications and constraints on the
  joints

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Contact Graph
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Data Structures for AssembliesExample

• Part
• Name motor
• URL motor.sat
• Transform Identity
• Part
• Name scanner
• URL scanner.sat
• Transform Identity
• List of joints between parts
• Joint Fixed
• Name potentiometer_sleeve_screw_potentiometer_to
  _frame
• BasePart potentiometer_sleeve
• AttachedPart screw_potentiometer_to_frame
• JointFeatures
• Point potentiometer_sleeve 0 0 0
• Point screw_potentiometer_to_frame 0 0 0
• Joint Revolute

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Assignment!

• Oct 6
• Mock up v1 of your Lego design
• Photos on Wiki
• Oct 10
• 3D model(s) for your Lego design
• Oct 13
• An assembly of your Lego design

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Introduction to Kinematics

• Kinematics study of motion independent of
  underlying forces
• Degrees of freedom (DoF) the number of
  independent position variables needed to specify
  motions
• State Vector vector space of all possible
  configurations of an articulated figure. In
  general, the dimensions of state vector is equal
  to the DoF of the articulated figure.

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Manipulator Joint Types

• 1 DOF Joint types
• Revolute
• Prismatic

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More Joint Types

• Many higher order joint types can be represented
  by combining 1-DOF joints by making axes intersect

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Forward vs. Inverse Kinematics

• Forward kinematics motion of all joints is
  explicitly specified
• Inverse kinematics given the position of the
  end effector, find the position and orientation
  of all joints in a hierarchy of linkages also
  called goal-directed motion.

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What CAD Systems do

• CAD systems analyze constraints
• But CAD systems, developers, and researchers do
  not mean mechanical constraint, they mean
  geometric location consistency
• Many designs called properly constrained by CAD
  systems are actually over-constrained
• Different CAD systems do this analysis different
  ways and can disagree about the same assembly

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What CAD Systems do

• How CAD Systems Test Constraints
• A closed chain of frames is set up
• A numerical test is done to see if the chain
  closes
• If, so, the assembly is called fully
  constrained
• Detailed tests for constraint/consistency
  problems are done by making small shifts and
  testing for interference
• Tolerance studies are done the same way
• Analysis requires detailed geometry
• Results depend on how the model was built

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Mathematical Model

• Basic Math
• Uses 4x4 matrices to relate adjacent frames
• Permits chaining together of parts
• same math is used to describe robots
• The matrix contains a rotational part and a
  translational part
• The matrix is designed to translate first and
  then rotate so that rotation does not change
  position of new frame
• This matrix is a subset of a more general
  projection matrix that includes perspective

• History
• Basic to Kinematics (Denavit Hartenberg)
• Used to model assemblies in 1970s
• S N Simunovic Masters Thesis, MIT, 1972
• Edinburgh University AI Lab robot assembly 1976
• Used by CAD researchers
• Steve Coons, 1960s
• Gossard and others, 1980s
• Used by CAD systems to locate surfaces wrt each
  other