ECE 470: Introduction to Robotics Homework 4
Question 1
The following two figures depict a two-link arm, that you have been working on since
Homework 1. You will be analyzing the dynamics under the assumption that the masses
m1 and m2 of the links L1 and L2, respectively, are lumped at the distal end of their link.
a) Determine the kinetic energy of the system (4 Points)
b) Determine the potential energy of the system (1 Points)
c) Use Lagrangian formulation to obtain the equation of motion (8 Points)
.
Figure 1
Question 2.
Robots can be designed to work on workpieces with enhanced efficacy and precision.
One common industrial application is surface treatment of components as illustrated in
Figure 2 showing robotic arms doing sanding and polishing.
Figure 2
Imagine you are tasked to design a robot to do polishing of the interior surface of
cylindrical components. You have decided to add one more link to point P in Figure 1
to manipulate a polishing tool as shown in Figure 3.
You have decided to select all links to be 0.25 m i.e. L1=L2=L3=0.25 m.
The inner diameter of the component ranges between 0.5 m to 0.6 m but unknow to you
as the component may come in different sizes.
(You may ignore the height of the workpiece and assume only constant Z-position. You
may also assume m1 and m2 to be negligible.)
a) Describe a control scheme to automate the manipulation the polishing tool in a
circular motion, contacting the inner surface at a specified contact force F. (4 Points)
b) Explain how you would select the torque range for the motors of Joint 2 and 3 with
a specified contact force F and the range of the inner diameter of the components.
(3 Points)
Figure 3
