Question

Problem 2 Given the 2-DoF PR robot shown, assuming no friction, link 1's center of mass is at its middle ( ½ L), and link 2's center of mass is 1/3L from the proximal end, imz (a) Derive the equations of motion in variable form to find the joint torques/forces F, and τ2-write answers below. b) Express the equations in matrix form using the formulation Clearly indicate each term in the matrices 0.2 .92 . π rad, θ2-0.1 rad, θ.. . 0.2!04 find F, and T2. Write answers below (d) If the joints experience friction: hydraulic joint 1 has a viscous damping coefficient of b 0.3 (this is the Bo part) and the motor joint 2 has a stiction of p part), find Fi and T2. Write answers below. N-S 02 Nm (this is the U (e) If in addition to the internal dynamics and friction, the end effector is required to apply a wrench of F 5 N,F, 10N, and tz 2 Nm,find Fi and tz. Write answers below.

Answer 1

Lame m2 Assuming seneralised coordinates as d and 82 ㄈ . Kinetic Energy of System Xo Potential Energy of system m (d +1 ) + (m2 t me) (Lat d08 . Lagrange (L) of system KE PE a) For generalised coordinate d For general ised coordinate 92 2 Equation (a) and ⑥ are the equattons of motion b) Expressing the equations in matrix form [o el fn,.matme).(F, 1 (di o (m,t m2 t me) o ㄈ C(4,4)

From e Fi (51312) 0-2 - (5+3+2) 981 96-1 M From eq 9 (d) IF the join ts expe riences frictfon in follo voing nays ') A viscous damping atjoint having b-03m ,'. Equation of motion for iointį ie A) changes to 2) the motor joint 2 has sttc tion of μ=04N-m Equation of motion for joint 2 ie⑤ changes to 9 e) For calculating the Joint Förces we have to calculate Jacobiarn for the Robot Frame Assign mernt D-H PARAMETER 乙2 9 2 0-1 o Litd 1-2 X2

010 o 00 Litd i o o o I o o oi οι ooI Litd Litd IJ(Li+d Fores on End-effector τe F2 ノMy 2 0 ら+2