EL5223 Homework 1 Solutions
1. (a) With 2 measured relative to the horizontal direction (i.e., at 2 = 0, the second link is parallel
to the ground), we nd the forward kinematics for the given robotic manipulator to be
x = D cos(2 )
(1)
y = d1 D sin(2 ).
(

Example of dynamics computation (Euler-Lagrange and Newton-Euler formulations):
Revolute-Prismatic-Revolute (RPR) manipulator (Problem 7.9)
Consider the Revolute-Prismatic-Revolute (RPR) manipulator shown in the figure below.
Let the coordinate system of

Newton-Euler formulation for dynamics of an n-link manipulator
In the Newton-Euler formulation, the force and torque equations for each link are written and then all the
forces and torques (including both the externally applied forces/torques and the cons

Example of dynamics computation (Euler-Lagrange and Newton-Euler formulations):
Prismatic-Prismatic-Prismatic (PPP) manipulator (3-link Cartesian manipulator) Solution to
Problem 7.7
Consider a Prismatic-Prismatic-Prismatic (PPP) manipulator (3-link Carte

Example of dynamics computation (Euler-Lagrange and Newton-Euler formulations):
Revolute-Revolute (RR) manipulator
Consider the Revolute-Revolute (RR) manipulator shown in the figure below.
The coordinate frames 0, 1, and 2 are shown in the figure. The jo

Example of dynamics computation (Euler-Lagrange and Newton-Euler formulations):
Revolute-Prismatic (RP) manipulator (Problem 7.8)
Consider the Revolute-Prismatic (RP) manipulator shown in the figure below.
Let the coordinate system of the base frame (fram

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b) By the associative property of matrix multiplication,
(x1 , x2 )x3 = x1 (x2 x3 ).
for x1 , x2 , x3 SO(n)
c) The n n identity matrix satises the third property.
d) Since xT x = xxT = I , it follows that xT = x1
2-8 For a rotation of about the x axis w

EL5223 Homework
1. Consider the two degree-of-freedom robotic manipulator shown below. This robotic manipulator is prismatic-revolute (PR), i.e., has two joints, the rst one being prismatic and the
second one being revolute. The prismatic joint can be use