McGill Dept of Mechanical Engineering MECH572A Introduction to robotics Lecture 9
MECH572A Introduction To Robotics Lecture 9 Dept. Of Mechanical Engineering
Review Velocity, Acceleration and Static Analysis Mapping between Cartesian and joint space Linear transformation J6=t J-W=T Joint rate+ Cartesian rate EE Wrench Joint force/torque Rate analysis Static analysis Jacobian matrix- General form for n-R manipulator e e xrl e2 xr2 en xrn Special case: 6R Decoupled Manipulator(PUMA) 311 o J
Review • Velocity, Acceleration and Static Analysis Mapping between Cartesian and joint space (Linear transformation) Jacobian Matrix – General form for n-R manipulator Special case: 6R Decoupled Manipulator (PUMA) Joint Rate Cartesian rate EE Wrench Joint force/torque Rate analysis Static analysis
Review Velocity, Acceleration and Static Analysis 6R Decoupled manipulator - Solve two linear systems of equations 3 equations 3 unknowns) Rate problem J110a +J120u =w J210a=c b J1ba=心 ju,8 11 Static problem =7 Jif=Ta-iinur
Review • Velocity, Acceleration and Static Analysis 6R Decoupled Manipulator -> Solve two linear systems of equations (3 equations 3 unknowns) Rate problem Static problem
Review Singularity analysis Based on the anal ysis of Jacobian matrix Singularity analysis of 6r decoupled manipulator General concept Conditioning analysis of J 12& J21 Acceleration Analysis 6=t-J6 6=J-l(t-J)
Review • Singularity Analysis - Based on the analysis of Jacobian Matrix - Singularity analysis of 6R decoupled manipulator - General concept – Conditioning analysis of J12 & J21 • Acceleration Analysis
Planar Manipulator 3-Revolute Planar Manipulator Properties 1)en/e2//e 2=03 3)ⅹ1,X2andx coplanar 八中 4)bl=b2=b3=0 5)al, az, and a3 none zero (Link length) O A1 XI
Planar Manipulator • 3-Revolute Planar Manipulator Properties: 1) e1 // e2 // e3 2) 1 = 2 = 3 3) X1, X2 and X3 coplanar 4) b1 = b2 = b3=0 5) a1, a2, and a3 none zero (Link length) e1 e2 e3 X1 X2 X3