+4 McGill Dept Of Mechanical Engineering MECH572 Introduction To robotics Lecture 4
MECH572 Introduction To Robotics Lecture 4 Dept. Of Mechanical Engineering
Review Concept of Screw Motion of a rigid body do=e d d A d w·p=w·a= constant (Qa-a Po 2(1-co6o) ford≠0
Review • Concept of Screw Motion of a rigid body O Q P P' A A' P0 dp e dA L
Review Use Plucker array to represent a line(screw axis) p1 xe Instantaneous motion Velocity Analysis: p=a+wx(p-a =a+92p-a) Angular velocity tensor S=QQ( Skew-symmetric W=vect()
Review • Use Plücker array to represent a line (screw axis) • Instantaneous Motion Velocity Analysis: Angular velocity tensor (Skew-symmetric)
Rigid-Body mechanics Instant Screw of rigid-Body Motion(cont'd) Define isa Consider 2 points a and p al+al P a=a“应=电 Ref Eq (26a&b) )4=2 Recall theorem 2.3. 4 If A 02=wwT-w|F1 Then A=-la 11+aa P 92a+(p-a)
Rigid-Body Mechanics • Instant Screw of Rigid-Body Motion (cont'd) Define ISA Consider 2 points A and P Recall Theorem 2.3.4 If Then Ref. Eq. (2.6a&b)
Rigid-Body mechanics Instant Screw of rigid-Body Motion(cont'd) Points on Isa p⊥=0 Pl‖ p ‖P2 P 92p=(a+ [> Ap=b p=0 A b=「a(1/|422a A Apo=A b ATA=S3+ww=-5+wT
Rigid-Body Mechanics • Instant Screw of Rigid-Body Motion (cont'd) Points on ISA O P'0