Consider the RR two-link planar manipulator shown below. 4x2 Y2 Yo a1 Y1 (12 21 To
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a) Derive the Jacobian to relate the joint velocities to the tool-point velocities.
b) Calculate the tool point linear velocity if joint 1 is rotating at 1.5 rad/s and joint 2
is rotating at 2 rad/s (a1 = 1.5, a2 = 3.5 θ1= 155 degrees, θ2 = -120 degrees).
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- Solve the following question by hand and without the use of AI. Use detailed mathematical expressions to solve the problem and please do not use AI. Thank You!Consider two robot-manipulators:• A SCARA robot with joints displacement range q1,2 = −90◦...90◦ and q3 = 0..10cm and links lengths L1,2=10 cm.• A Cartesian robot with joint displacements’ range q1,2,3 = 0..10 cm.Which statement is correct?1) The Cartesian robot has a larger workspace.2) It is not possible to judge the workspace based on the information provided.3) Both robots have revolute joints.4) The SCARA robot has a larger workspace.Consider the following mathematical model of a single-link flexible joint robotic manipulator (shown in the following figure) where the output of the system is y(t) = q₁(t), and I, m, g,l,k and are constants. lä(t) + MgLsin(q1(t)) + k(q1(t) - 92(t)) = 0 Jäz(t)-k(q1(t)-92(t)) = u(t) a) Linearize the nonlinear dynamics at the working point q₁ = q₁ = 92 = 92 = 0. b) For parameters I = 2,J = 1, k = 1, g = 10, M = 0.1, L = 1, find the transfer function from input u to the output y. 92 91 M, I
- PLEASE SOLVE ALL THE QUESTION WITH KEYBORD AND GIVE ME FULL ANSWER WITH JUST KEYBOARD NOT HAND WRITTING , THANK YOUA manipulator’s end-effector position is calculated as follows:x = q0 cos q1 + l2 cos(q1 + q2),y = q0 sin q1 + l2 sin(q1 + q2),where q0,1,2 represent joint displacements and l2 is a constant positive parameter.Which of the following describes this manipulator:1) This is a robot-manipulator with 3 revolute joints.2) This is a robot-manipulator with 2 revolute and 1 prismatic joints.3) This is a robot-manipulator with 1 prismatic and 3 revolute joints.4) This is a robot-manipulator with 2 revolute joints. A robot’s end-effector’s tool position is defined asx = L1 cos(q1) + q3 sin(q1 + q2)where L1 = const, q1 = q1(t), q2 = q2(t) and q3 = q3(t) with t defining time. Calculate ∂x / ∂q3 1) it is impossible to calculate as the equation for the y and z positions are missing.2) cos(q1 + q2).3) it is impossible to calculate as time is not given.4) sin(q1 + q2).As8