Manipulator Dynamics-1

Different configurations need different torques to

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online