Question

Introduction to Robotics

EXERCISES 6.1 [12] Find the inertia tensor of a right cylinder of homogeneous density with respect to a frame with origin at the center of mass of the body.

Please solve this with clear steps, I will rate!

Answer 1

We know the cylinder will lay in xay plane, with an angle o with the xraxis. let assunse 2 is high = It has linear density - t - dus = Ando o Assunge x = 8 coso; y =rson o© Londo Bec ) - and o = constant . we get Ixx = J dws (y² +22) = (dwyr Iyy = (dwg (2² +22) = (dmar 122 = 1 du(x²+4) Iny = -5dway @ ③ .. we can write by substuting eq@, in above - Idy = d.s0n? o do = sundo 419 Isyy = me cos o Izz = x order = my Ixy = -A cosesino do = - sono cos niin - Inertia tensor will be written as . We supo mi sono coso on - sino caso we cost o o ㅍ 12 22 -412 4 2 wa