Manipulator Dynamics-1

Different configurations need different torques to

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Unformatted text preview: configurations need different torques to achieve accelerations: consider 1 below 1 Ze Xe D1 Z1 X1 Z2 D0 • Z0 X2 D2 X0 The moment of inertia is related to the mass distribution of the links and its motions in particular coordinate frames Inertia tensor • • Using inertia to describe mass distribution with respect to a coordinate Inertia tensor in {A} can be expressed as distance × mass , • • , =∭ , , are called mass moments of inertia are called mass products of inertia + )ρdv, =∭ =∭ • • + )ρdv, =∭ + ρdv i, j = x, y, or z; i≠j ρ is the density of the material If we chose the frame in such a way that the products of inertias are all zero, the axes are called principal axes, and mass moments are called the principal moments of inertia )ρdv Inertia tensor examples (1) ̂ Which one has greater • ̂ , , or ? Calculate the inertia tensor for the following object and the attached frame. Assuming density to be even ̂ Inertia tensor examples (2) = + )ρdxdydz = + )ρwdydz = + )ρwdz =( hw + lw)ρ = l +4 h ) • What if we remove the frame to a new place as shown below? • How can we make the mass products of inertia all zero? ̂ = = ρdxdydz...
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