Two-link Planar Arm

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Two-link Planar Arm
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Two-link Planar Arm
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Joint Space Dynamic Model
Viscous friction torques
Actuation torques
Coulomb friction torques
Force and moment exerted on the environment
Coriolis/ centripetal torque
Multi-input-multi-output Strong coupling
Nonlinearity
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Direct Dynamics and Inverse Dynamics

• Direct dynamics
• Given joint torques and initial joint position
  and velocity, determine joint acceleration
• Useful for simulation
• Inverse dynamics
• Given joint position, velocity and acceleration,
  determine joint torques
• Useful for trajectory planning and control
  algorithm implementation

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Two-link Planar Arm Inverse Dynamics (Example
4.2)
Matlab Toolbox
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Two-link Planar Arm Inverse Dynamics (Example
4.2)
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Two-link Planar Arm Direct Dynamics (Example 4.2)

• Robot toolbox
• Case 1 no actuating torques
• Case 2 actuating only the first joint
• Case 3 simulate puma560 by yourself

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Matlab Toolbox

• Useful functions
• Accel (pp 20) Compute manipulator forward
  dynamics
• Coriolis(pp 22) Compute the manipulator
  Coriolis/centripetal torque components
• Gravload(pp 33)Compute the manipulator gravity
  torque components
• Itorque(pp40) Compute the manipulator inertia
  torque component
• Rne(57) Compute inverse dynamics via recursive
  Newton-Euler formulation
• Simulink library
• Roblocks.mdl

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Two-link Planar Arm Dynamic Model
L1 link( 0 1 0 0 0, 'standard') D-H
param L2 link( 0 1 0 0 0,
'standard') L1.m 50 link mass L2.m
50 L1.r -0.5 0 0 center of mass
referred to the link frame L2.r -0.5 0
0 L1.I 0 0 10 0 0 0 inertia
tensor L2.I 0 0 10 0 0 0 L1.Jm
0.01 inertia of motor L2.Jm 0.01 L1.G
100 gear reduction ratio L2.G 100 global
mytl mytl robot(L) mytl.gravity0 9.81 0
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Joint Space Dynamic Model
Viscous friction torques
Actuation torques
Coulomb friction torques
Force and moment exerted on the environment
Coriolis/ centripetal torque
Multi-input-multi-output Strong coupling
Nonlinearity