ECE 215 - Models of Robotic Manipulation Homework 5 2022
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ECE 215 - Models of Robotic Manipulation
Homework 5
2022
1. Consider frame {B} rotating relative to frame {A} in the Z − Y − X Euler angle representation.
(a) Compute the angular velocity using the formula for differentiation of a compound rotation matrix
where
(b) Obtain the Jacobian by expressing the angular velocity in the form
where
(c) Compute the singularities of the rotation.
2. Consider the RPR robotic manipulator of Example 3.4 in the book.
(a) Compute the velocity of the tip of the end effector as a function of the joint rates, θ˙1 and θ˙3 , and link offset rate d˙2 . Express it in frames {0} and {3}.
(b) Determine the Jacobian of the tip velocity expressed in frame {3} and compute any singularities of the manipulator.
2022-02-11