MECH572A Introduction To Robotics - PowerPoint PPT Presentation

1 / 32
About This Presentation
Title:

MECH572A Introduction To Robotics

Description:

Robotic Kinematics Overview. Basic Concepts. Robot Kinematics - Study robot motion without resorting to ... Direct Kinematics. Some useful properties of Qi ... – PowerPoint PPT presentation

Number of Views:124
Avg rating:3.0/5.0
Slides: 33
Provided by: Main160
Category:

less

Transcript and Presenter's Notes

Title: MECH572A Introduction To Robotics


1
MECH572AIntroduction To Robotics
  • Lecture 5

2
Midterm Exam
  • Date Time 1900 - 2100 ,Oct 25, 2004
  • Open Book
  • Chapters 2 3 of the text book
  • Note Regular lecture will take place 1800
    1845 on Oct 25

3
Review
  • New concepts
  • Twist of rigid body
  • Wrench (static analysis)
  • Instantaneous Screw of rigid-body motion
  • Define by direction one point
  • Similarity between Velocity and Force/Moment
    Analysis
  • Screw-like force and moment property Wrench axis

4
Review
  • Acceleration Analysis
  • Fixed reference frame
  • Moving Reference frame
  • Corilios term in the expression
  • Basics in Rigid Body Dynamics
  • Mass properties - Mass 1st 2nd Moment
    Parallel Axes Theorem
  • Principle
    Axes/Moments (Eigenvectors/values)
  • Equation of Motion Newton-Euler Equations

Acceleration tensor
5
Robotic Kinematics Overview
  • Basic Concepts
  • Robot Kinematics - Study robot motion without
    resorting to force and mass properties. Dealing
    with position, velocity and acceleration
  • Kinematic Chain - A set of rigid bodies connected
    by kinematic pairs
  • Kinematic Pairs
  • Upper Pair - Line/point contact (gear,
    cam-follower)
  • Lower Pair - Surface contact (revolute, prismatic)

6
Robotic Kinematics Overview
  • Basic Concepts (cont'd)
  • Typical Lower Kinematic Pairs
  • Revolute (R) - 1 Dof (Rotation)
  • Prismatic (P) - 1 Dof (Translation)
  • Cylindrical (C) - 2 Dof (Rotation
    Translation)
  • Helical (H) - 1 Dof (Coupled
    Rotation/Translation)
  • Planar (E) - 2 Dof (Translation
    in 2 directions)
  • Spherical (S) - 3 Dof (Rotation in
    3 directions)

7
Robotic Kinematics Overview
  • Basic Concepts (cont'd)
  • Two Basic Types of Kinematic Pairs - R P
  • All six lower pairs can be produced from
    Revolute (R) and Prismatic (P)

Sliding pair Prismatic (P)
Rotating pair Revolute (R)
8
Robot Kinematics Overview
  • Robot Manipulators
  • Kinematic Chains Link Joint
  • Rigid bodies
    Kinematic Pairs
  • Basic Topologies of Kinematic Chain

Necklace
Open Chain
Tree
9
Robot Kinematics Overview
  • Basic Problems in Robotic Kinematics
  • Direct Kinematics
  • Inverse Kinematics

px, , py,pz
?????
Joint Variables
Cartesian Variables
Direct
? x
(Joint)
(Cartesian)
Linear relationship between Cartesian rate of EE
and joint rates
Inverse
10
Denavit-Hartenberg Notation
  • Purpose
  • To uniquely define architecture of robot
    manipulator (Kinematic chains)
  • Assumptions
  • Links 0, 1, , n - n1 links
  • Pairs 1, 2, , n - n pairs
  • Frame Fi (Oi - Xi -Yi -Zi) is attached to
    (i-1)st frame
    (NOT ith frame)

11
Denavite-Hartenberg Notation
  • Definition of Axes
  • Zi - Axes of the pair (Rotational/translational)

Zi
Zi
12
Denavite-Hartenberg Notation
  • Definition of Axes (cont'd)
  • Xi - Common perpendicular to Zi1 and Zi
    directed from Zi1 to Zi (Follow right hand
    rule if intersect)
  • Yi Zi ? Xi

Zi-1
Zi
Xi undefined
(d)
13
DH Notation
  • Joint Parameters Joint Variables
  • ai - Distance between Zi and Zi1
  • bi - Z-coordinate of Zi and Xi1 intersection
    point (absolute value distance between Xi and
    Xi1 )
  • ?i - Angle between Zi and Zi1 along Xi1
    (R.H.R)
  • ?i - Angle between Xi and Xi1 along Zi
    (R.H.R)
  • Joint Variables
  • ?i - R joint
  • bi - P joint

14
DH Notation
  • Summary

15
DH Notation
  • Summary Prismatic joint

Xi1
bi Variable ?i - Constant
16
DH Notation
  • Example - PUMA

17
DH Notation
  • Example - PUMA

18
DH Notation
  • Example PUMA
  • DH Parameters of PUMA
    Robot

i ai bi ?i ?i
1 0 b1 90 ?1
2 a2 0 0 ?2
3 a3 b3 90 ?3
4 0 b4 90 ?4
5 0 0 90 ?5
6 0 b6 ? ?6
19
DH Notation
  • Example - Stanford Arm

20
DH Notation
  • Example - Stanford Arm

21
DH Notation
  • Example - Stanford Arm (cont'd)
  • DH Parameters of Stanford
    Arm

i ai bi ?i ?i
1 0 b1 90 ?1
2 0 b2 90 ?2
3 0 b3 (var) 90 90
4 0 0 90 ?4
5 0 b5 0 ?5
6 0 b6 0 ?6
22
DH Notation
  • Summary

ith pair R joint P joint Number of parameters/variable
Joint Parameters (Constant) ai, bi, ?i ai, ?i, ?i 3
Joint Variable (Changing) ?i bi 1
If there are n joint, there will be 3n joint
parameters and n joint variables
23
DH Notation
  • Relative Orientation and Position Analysis
  • Orientation

? i about Zi
(a)
?i about Xi'
(b)
Rotation Decomposition (a) (b)
24
DH Notation
  • Relative Orientation and Position Analysis
  • Orientation (cont'd)
  • (Xi, Yi, Zi) (Xi', Yi', Zi')
  • (Xi', Yi', Zi') (Xi1, Yi1, Zi1)

25
DH Notation
  • Relative Orientation and Position Analysis
  • Orientation (cont'd)

26
DH Notation
  • Relative Orientation and Position Analysis
  • Position
  • To find the position vector ai in Fi frame
    (position vector connecting Oi to Oi1

27
DH Notation
  • Relative Orientation and Position Analysis
  • Position
  • Observation

Changing
Constant
28
DH Notation
  • Relative Orientation and Position Analysis
  • Summary
  • Orientation
  • Position

29
Direct Kinematics
  • 6-R Serial Manipulator
  • Problem description
  • Known ?1 ?n, find Q and p in the
    base frame

30
Direct Kinematics
  • 6-R Serial Manipulator
  • 1. Orientation
  • With DH Parameter defined, Q1, Q6 can
    be calculated.

Similarity transformation to individual frame
Abbreviated notation Qi Qii
31
Direct Kinematics
  • 6-R Serial Manipulator
  • 2. Position
  • 3. Homogeneous form (position
    orientation)

32
Direct Kinematics
  • Some useful properties of Qi
Write a Comment
User Comments (0)
About PowerShow.com