Question Description

1. A robot manipulator is used to assemble a car headlight. Tasks for the manipulator are described in a fixed frame A. A frame B is attached to the robot end-effector. The current configuration of the end-effector is described by the rigid-body transformation   0.560620 −0.303214 0.770562 2.587600  0.786016 0.487644 −0.379977 2.861610   gab =   −0.260546 0.818697 0.511714 1.998900  0 0 0 1 (a) Consider a twist described in the frame B by Tb = description of this twist in the frame A.  5 −1 −3 2 1 4 T . Find the (b) Assume the robot is asked to exert a wrench which is described in the frame B by  T Wb = −3 −4 −2 1 −1 −5 . Find the description of this wrench in the frame A. Figure 1: 3-DOF manipulator for Problem 2. 2. Consider the manipulator in Figure 1. Take the arrows on the joint axes as the indication of the direction of rotation (for joints 2 and 3 the direction of the arrow on the axis is not consistent with the direction of the rotation marking). 1 (a) Conveniently choose frames S and T , the reference configuration, and identify all the joint twists. Define the kinematic parameters as you need them. (b) Compute the orientation of the tool frame as a function of the joint displacements and the kinematic parameters you chose. Chapter 5. Velocity Kinematics and Statics 215 (c) Compute the position of the origin of the tool frame as a function of the joint displacements and the kinematic parameters you chose. θ1 θ5 θ6 θ4 θ2 θ3 (a) Rehabilitation robot ARMin III . Figure courtesy of ETH Zürich. Figure 2: Rehabilitation robot ARMin III ŷt x̂t L θ1 {c} Last link L L L ẑt {t} x̂0 ẑc x̂c ẑ0 ŷ0 {0} ŷc Elbow link L θ5 θ6 θ2 L L L θ4 L θ3 L (b) Kinematic model of the ARMin III. Figure 3: Kinematic model of the ARMin III Figure 5.31: The ARMin III rehabilitation robot. 3. Consider the manipulator in Figure 2 and the kinematic model of the robot in Figure 3. Take the configuration in Figure 3 as the reference configuration. The figure also shows the location 0, 0, 0, 0, 1) and tip = (0, 1, 0, 1, 1, 0). Find the joint forces and torques of frames (1, S (frame {0}) and FT. 2 May 2017 preprint of Modern Robotics, Lynch and Park, Cambridge U. Press, 2017. http://modernrobotics.org (a) Compute all the joint twists. (b) Compute the orientation of the tool frame as a function of the joint displacements and the kinematic parameters you chose. (c) Compute the position of the origin of the tool frame as a function of the joint displacements and the kinematic parameters you chose. 4. Consider again the manipulator in Figure 1. Place the frame S at the base of the manipulator, with its z axis corresponding to the axis of Joint 1 and its x axis parallel to the axis of Joint 2. Further, assume that Link 3 lies in the y-z plane of frame S and that the end-effector frame T is located at the very end of the link 3. Also, assume that the lengths l1 , l2 , and l3 of the links 1, 2 and 3, respectively, satisfy l1 > l2 > l3 . Sketch or describe the reachable workspace of the manipulator. Ignore possible collisions between links and assume every joint can rotate for full 360◦ . 5. Consider the Kraft Viper manipulator in Figure 4. (a) Conveniently choose frames S and T , the reference configuration, and identify all the joint twists. Ignore the gripper jaw motion and define the kinematic parameters as you need them. (b) Compute the position of the origin of the tool frame as a function of the joint displacements (and the kinematic parameters you chose). Figure 4: Kraft Viper manipulator for Problem 5. 3 Problem 1 {{ 0.560620, -0.303214, 0.770562, 2.587600}, { 0.786016, 0.487644, -0.379977, 2.861610}, {-0.260546, 0.818697, 0.511714, 1.998900}, { 0, 0, 0, 1}} …
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