Manipulator Dynamics 3 Instructor Jacob Rosen Advanced Robotic
Manipulator Dynamics 3 Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - Solution Procedure • Step 1 - Calculate the link velocities and accelerations iteratively from the robot’s base to the end effector • Step 2 - Write the Newton and Euler equations for each link. • Outward Iterations Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - Solution Procedure • Step 3 - Use the forces and torques generated by interacting with the environment (that is, tools, work stations, parts etc. ) in calculating the joint torques from the end effector to the robot’s base. • Inward Iterations Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - Solution Procedure • Error Checking - Check the units of each term in the resulting equations • Gravity Effect - The effect of gravity can be included by setting. This is the equivalent to saying that the base of the robot is accelerating upward at 1 g. The result of this accelerating is the same as accelerating all the links individually as gravity does. Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Inward iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Inward iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Inward iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Inward iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example • Inward iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Iterative Newton-Euler Equations - 2 R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Equation of Motion – Non Rigid Body Effects • Viscous Friction • Coulomb Friction • Model of Friction Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Velocity / Force Transformation - Wrist / Sensor / Tool • Note: The three frames including the tool {T}, the F/T sensor {S} and the wrist {W} (typically the last frame of the manipulator i. e. frame 6 of a DOF arm) are all assigned to different points of a rigid body and therefore they are all rigidly connected. As such they share the same angular velocity and the realtive angular velocity is equal to 0. Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Velocity / Force Transformation - Wrist / Sensor / Tool • The expression of generalized velocity (linear and angular) along with the generalized load (force and torque) at one point of a rigid body (i. e. point B) based on their values at a different point (i. e. point A) are expressed as: Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Velocity / Force Transformation - Wrist / Sensor / Tool 0 Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Velocity / Force Transformation - Wrist / Sensor / Tool • This relationship can be inverted such that Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Velocity / Force Transformation - Wrist / Sensor / Tool Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
Velocity / Force Transformation - Wrist / Sensor / Tool • This relationship between the velocity transformation matrix is given by Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA and the force
Velocity / Force Transformation - Wrist / Sensor / Tool • Give: A force/torque sensor is typically placed between the wrist and the tool gripper holding a tool. This sensor can measure simultaneously force and torques along 3 orthogonal axis • Find: the forces and torques applied at the tip of the tool • Solution Calculate the inverse of and find Instructor: Jacob Rosen Advanced Robotic - MAE 263 D - Department of Mechanical & Aerospace Engineering - UCLA
- Slides: 50
