Mechatronics 1 Weeks 5,6, & 7

Learning Outcomes By the end of week 5-7 session, students will understand the dynamics of industrial robots.

Course Outline General understanding of moment, force and moment of inertia which occur in a robot. Interpretation of robot dynamic behaviour and dynamic equation. Introduction to Newton-Euler dynamic equation. Newton Euler approach. Forward iteration & backward iteration algorithms. Implementation of Newton Euler approach and its physical interpretation.

Why Dynamics ? Instant response never happens in a real world. Various postures, tasks and payloads. Fundamental problem to solve, prior to designing a control system  robot controller. Never expect to have a good control system if we don’t know the dynamic behaviour of the robot. There is no such task accomplishment if the control system is poor.

Dynamics (1) It concerns about forces/ torques excerted in a robot movement.

Dynamics (2) Dynamic components : Mass & InertiaMass & Inertia FrictionFriction InductanceInductance

Dynamics (3) Mathematical equations describes the dynamic behavior of the manipulator –For computer simulation –Design of suitable controller –Evaluation of robot structure –Joint torques Robot motion, i.e. acceleration, velocity, position

Dynamics (4) Forward Dynamics Inverse Dynamics

Dynamics (5) Lagrange Euler –Closed form. –Tedious and heavy computing burden. Newton Euler –Recursive Form. –Efficient computing burden. –Suitable for real time application.

Physics Quick Review Mass Moment of Inertia Centre of Mass Gravity Physical interpretation in a robot case.

Physics Quick Review Forces & Torques Newton Law Kinetic & Potential Energies Physical interpretation in a robot case. Posture of robot (link configuration)

Lagrange-Euler - Principle Lagrange-Euler Formulation –Lagrange function is defined K: Total kinetic energy of robot P: Total potential energy of robot : Joint variable of i-th joint : first time derivative of : Generalized force (torque) at i-th joint Physical interpretation

Newton - Euler Intuitively, more understandable. Composed of 2 steps –Forward iteration to obtain information on position, velocity and acceleration. –Backward iteration to obtain information on forces and torques. Frames attached to the corresponding links are considered moving to each other while the robot moves.

Basic Concept The movement of lower joints affect the movement of upper (distal) joints. Hence, the movement of upper joints are the functions of lower joint movement. Forces and torques occur in the upper joints affect the forces and torques occur in the lower joint (lower joints suffer forces/ torques exerted by the upper joints). All information are presented in vector components.

Revealing Kinematic Information

Forward Recursive w.r.t. Inertial Frame Notes : For i = 1 to n; n = number of joints; Input :

Physical meaning of forward recursive.

Forces/ Torques Exerted in a Robot

Backward Recursive w.r.t Inertial Frame For i = n to 1; n = number of joints.

Physical meaning of backward recursive.

Manipulator Dynamics Dynamics Model of an n-link Arm The Acceleration-related Inertia matrix term, Symmetric The Coriolis and Centrifugal terms (negligible for a slow movement) The Gravity terms Driving torque applied on each link

Physical meaning of a complete dynamic model of an n link arm.

Forward Recursive w.r.t. Own Frame

Backward Recursive w.r.t. Own Frame

Dynamic Simulation Process Dynamic Equation Integration (ODE)