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Unformatted text preview: Massachusetts Institute of Technology Department of Mechanical Engineering 2.12 Introduction to Robotics Problem Set No.3 Out: October 3, 2005 Due: October 12, 2005 Problem 1 Shown below is a construction robot having two revolute joints and one prismatic joint. Notice that the axis of the prismatic joint has an offset of from the first revolute joint at the origin O. Namely, the distance between point O and point A is , a constant, and the angle between OA and AB is 90 degrees, a constant as well. Joint 2 is a prismatic joint, whose displacement is given by distance d , a variable. Using the geometric parameters and joint displacements shown in the figure, answer the following questions. 1 A 1 A Joint 1 Link 3 Link 2 Link 1 Joint 3 Joint 2 Link 0 3 A 1 θ e φ y 3 θ x ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ e e y x d B A O Link 0 1 A Figure 1 Construction robot with two revolute joints and one prismatic joint (a) Obtain the kinematic equations relating the end-effecter position and orientation to the...
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- Fall '05
- Mechanical Engineering, inverse kinematics problem, Articulated robot