Manipulator Dynamics

Question 1

Define an inertia tensor

Answer 1

Inertia of a rigid body relative to a reference frame

Question 2

Define parallel axis theorem

Answer 2

Relates the inertia tensor in a frame within the origin to a frame in the centre of mass with respect to another frame {A}

Question 3

If we have the location of centre of mass relative to {A}, how can the interia tensor be defined?

Answer 3

aI = cI + M[PcT Pc I3 - Pc PcT]

aI = inertia tensor with respect to A

Question 4

The inertia tensor is made up 2 kinds of scalar elements, what are they?

Answer 4

Mass moments of inertia (Ixx, Iyy, Izz)
Mass products of inertia (Ixy, Ixz, Iyz)

Question 5

What is the difference between the closed form and iterative approach of dynamics?

Answer 5

Iterative numerically computes the values via the newton euler algorithm
Closed form symbolically computes the values via the newton euler algorithm

Question 6

How can we include gravity on the joints?

Answer 6

Set 0vdot0 as G
The acceleration of joint 0 should be 9.81 but in the opposite direction

Question 7

How do we find the torques of the maniupulators in dynamics?

Answer 7

Perform outward iteration (start from frame 0)
to find w,w_dot, v_dot, v_Cdot, F and N

Then perform inward iteration(highest frame number) to find ƒ,n and torque