McGill Dept of Mechanical Engineering MECH572A Introduction To robotics Lecture 5
MECH572A Introduction To Robotics Lecture 5 Dept. Of Mechanical Engineering
Midterm exam Date&Time:19:00-21:00Oct25.2004 Open Book Chapters 2&3 of the text book Note: Regular lecture will take place 18: 0018: 45 on Oct 25
Midterm Exam • Date & Time: 19:00 - 21:00 ,Oct 25, 2004 • Open Book • Chapters 2 & 3 of the text book Note: Regular lecture will take place 18:00 –18:45 on Oct 25
Review New concepts Twist ofrigid body t=/w Wrench(static anal ysis W三 Instantaneous Screw of rigid-body motion Define by direction 间+ one point Po Similarity between velocity and Force/Moment Analysis f Screw-like force and moment property: Wrench axis
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
Review Acceleration Anal ysis Fixed reference frame 阝=+(+92)(p-a W≡+ Acceleration tensor 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 =Icw+wxIcw
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
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) ower Pair-Surface contact (revolute, prismatic
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)
Robotic Kinematics overview Basic Concepts (contd 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()-3 Dof (Rotation in 3 directions)
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)
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) Rotating pair Sliding Revolute(r) Prismatic (P)
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) Rotating pair – Revolute (R) Sliding pair – Prismatic (P)
Robot Kinematics overview Robot manipulators Kinematic chains: Link Joint Rigid bodies Kinematic Pairs Basic Topologies of Kinematic Chain Open Chain ee ecklace
Robot Kinematics Overview • Robot Manipulators Kinematic Chains : Link + Joint Rigid bodies Kinematic Pairs • Basic Topologies of Kinematic Chain Open Chain Tree Necklace
Robot Kinematics overview Basic problems in robotic Kinematics Direct Kinematics Inⅴ erse Kinematics Z End effector E px, py, p: P ,,y 0 Base 0 Joint variables Cartesian B arabis y X=f(0) Direct (oint)8 X(Cartesian Linear relationship between Cartesian rate of ee and joint rates
Robot Kinematics Overview • Basic Problems in Robotic Kinematics Direct Kinematics Inverse Kinematics . . . X Y Z O Base End Effector 1 2 i n = z y x p p p x = n . . . 2 1 θ px, , py,pz Joint Variables Cartesian Variables θ θ f x = Linear relationship between Cartesian rate of EE and joint rates x Direct Inverse x = f(θ) (Joint) (Cartesian)
Denavit-Hartenberg notation Purpose To uniquely define architecture of robot manipulator (Kinematic chains Assumptions Links: 0.1..n n+l links Pairs: 1.2...n n pairs Frame Fi(Oi-Xi-Yi-Zi is attached to(i-1)st frame (NOT ith frame)
Denavit-Hartenberg Notation • Purpose – To uniquely define architecture of robot manipulator (Kinematic chains) • Assumptions – Links : 0, 1, …, n - n+1 links – Pairs: 1, 2, … , n - n pairs – Frame Fi (Oi - Xi -Yi -Zi) is attached to (i-1)stframe (NOT ith frame)
