3 Problem 3: Using the Lagrangian method, obtain the equations of motion in terms of the torque for the2-DOF robot arm shown in Figure 3, given the total kinetic energy K and total potential energy P asshown below. The center of mass for each link is at the center of the link. The moments of inertiaare I1₁ and 1₂.Yo4₁P=m₁g S₁ + m2g|l₁S₁ +41,4The total potential energy P of the system is+1/2/512)myCThe total kinetic energy K is1K = 0² ( _m₂l² + _m²l² + _m₂l² + 1/ m₂hhc₂ )12/1/2+ 0² ( 1 m₂l² ) + this ( m₂l² + / m₂/C₂)0₁У1BT₂Dm₂Figure 3 for Problem 30₂where, S1 = sin(01), C1 = cos(01), S12 = sin(0₁+02) and similarly others.

The total kinetic energy and the total potential energy are given for the system. The expression for…

Problem 3: Using the Lagrangian method, obtain the equations of motion in terms of the torque for the 2-DOF robot arm shown in Figure 3, given the total kinetic energy K and total potential energy P as shown below. The center of mass for each link is at the center of the link. The moments of inertia are 1₁ and 1₂. The total kinetic energy K is 4,4 K m²l²2 xo mi C 1 x = 0² ( @_m² ² + + m₂l² + 1/{m₂l² + = m₂ll₂ (₂) + 0² ( ½ m²l²³) + Ö‚Ò₂ (²m²l² + ½ m²ll2C₂) B T₂ * ។ D m₂ x1 0₂ Figure 3 for Problem 3 The total potential energy P of the system is h P=m₁g / S₁ + m28 (4₁S₁ + 1/25₁2) where, S1 = sin(01), C₁ = cos(01), S12 = sin(01+02) and similarly others.

Problem 3: Using the Lagrangian method, obtain the equations of motion in terms of the torque for the 2-DOF robot arm shown in Figure 3, given the total kinetic energy K and total potential energy P as shown below. The center of mass for each link is at the center of the link. The moments of inertia are 1₁ and 1₂. The total kinetic energy K is 4,4 K m²l²2 xo mi C 1 x = 0² ( @_m² ² + + m₂l² + 1/{m₂l² + = m₂ll₂ (₂) + 0² ( ½ m²l²³) + Ö‚Ò₂ (²m²l² + ½ m²ll2C₂) B T₂ * ។ D m₂ x1 0₂ Figure 3 for Problem 3 The total potential energy P of the system is h P=m₁g / S₁ + m28 (4₁S₁ + 1/25₁2) where, S1 = sin(01), C₁ = cos(01), S12 = sin(01+02) and similarly others.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter10: Fixed-axis Rotation

Section: Chapter Questions

Problem 112AP: A system of point particles is rotating about a fixed axis at 4 rev/s. The particles are fixed with...

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