MCTE 4352
ROBOTICS
SEM II 2020/2021
COURSE MINI PROJECT
(This project covers LO1 - LO5)
Figure 1 shows a planar 3-DOF robotic leg standing on the ground.
Figure 1: Leg Robot
Three joint angles, 𝜃1 , 𝜃2 , 𝜃3 , all measured from the ground are used as an independent set of
generalized coordinates uniquely locating the system. Figure 1(b) shows the front view
including the actuators and the transmission mechanisms.
Actuator 1 generates torque, 𝜏1 between link 0 and link 1. Note that the body of Actuator 1 is
fixed to link 0, while its output shaft is connected to link 1.
Actuator 2 is fixed to Link 3, and its output torque, 𝜏2 is transmitted to Joint 2, i.e., the knee
joint, through the mass-less belt-pulley system with a gear ratio of 1:1.
Actuator 3 is fixed to Link 3, while its output shaft is connected to Link 2. All actuator torques
𝜏1 , 𝜏2 , 𝜏3 are measured in a right-hand sense, as shown by the arrows in the figure.
Displacements of the individual actuators are denoted 𝜑1 , 𝜑2 , 𝜑3 , and are measured in the same
direction of the torque. The location of the hip, i.e. Link 3, is represented by the coordinates of
its center of mass, 𝑥ℎ , 𝑦ℎ , and angle α measured from the base coordinate system fixed to Joint
1, as shown in the figure.
a) Develop the endpoint coordinates 𝑥ℎ and 𝑦ℎ as functions of α and formulate the inverse
kinematics solution for joint variables 𝜃1 , 𝜃2 , 𝜃3 as functions of α.
b) Assume the trajectory of the hip, α is shown as below.
Figure 2: Hip joint trajectory
Time (s)
0
0.05
0.1
0.15
0.2
0.25
0.27
0.3
0.35
0.4
0.45
0.5
α(t)
35
33
25
10
0
-7
-9
-6
13
28
35
33
Develop the trajectory of all joints (𝜃1 , 𝜃2 , 𝜃3 ) to ensure the path of the α will be
followed. You may use any suitable software to plot the graphs of position, velocity,
and acceleration of each joint variable.
c) Formulate the expressions to relate the actuator angular velocities, 𝛷̇1 , 𝛷̇2 , 𝛷̇3 and the
velocities of the hip (𝑥̇ ℎ , 𝑦̇ ℎ )
d) Develop the dynamic force model for each of the joint for the leg robot (𝑇1 , 𝑇2 , 𝑇3 ) and
suggest the best actuator to be used for Actuator 1, 2 and 3. You need to provide the
torque calculation of the system and the specification of actuator model that you
propose.
e) Design the force control algorithm for the leg robot. Draw the flowchart and the block
diagram of the proposed control system.
This project is to be done in pair. Prepare a report to answer all questions.