TRC4800/MEC4456 Robotics PC 8: Joint ControlR

Java Python Department of Mechanical and Aerospace Engineering

TRC4800/MEC4456 Robotics

PC 8: Joint Control

Objective: To model the dynamics and master the partitioned controller design of robotic systems.

Problem 1. Prove that the torque equation for the mechanism shown in Figure 1 is

where gear ratio

What are the effective inertia and effecting damping terms of the system?

Figure 1: Mechanism for Problem 1.

Problem 2. The torque equation for joint 1 for the manipulator shown in Figure 2 is

where masses are point masses at the end of each link.

Figure 2: A two-link RR manipulator.

Compute the variation (as a percentage of the maximum) of inertia “seen" by joint 1 of the manipulator as it changes confi TRC4800/MEC4456 Robotics PC 8: Joint ControlR guration. Use the numerical values

l1 = l2 = 0:5 m m1 = 4:0 kg            m2 = 2:0 kg

Consider that the robot is direct drive and that the rotor inertia is negligible.

Hint: Find the manipulator's mass matrix.

Repeat the calculation for the case of a geared robot (use η = 20) and a rotor inertia of Im = 0:01 kgm2.

Problem 3. In a system like that shown in Figure 3, find the criteria for KD and KP of a PD controller such that the system is never unstable and never underdamped. Design the PD control to control τ (solve the torque balance equations for τ, rather than τm).

The system possesses an un-modelled resonance due to an end-point stiffness K (on the non motor side, not shown in figure). Any damping terms in the system are negligible. Also, η = R1/R2 >1.

Figure 3: Mechanical model of a DC torque motor connected through gearing to inertial load