600.445 Homework 1

PROBLEM 1:

Consider the problem of drilling guide holes for the distal cross-locking screws in intra-medulary nails, as shown on the videotape in class. In the tape, two manual techniques are shown.

What are some of the criteria by which a system to assist surgeons in carrying out this procedure should be judged?

Discuss the strengths and weaknesses of each of the shown techniques relative to these criteria. How do they compare to each other?

Outline at least one method or system that might significantly improve upon the two methods shown. Include a sketch or two and discuss your method's strengths and weaknesses relative to the previous ones.

Outline how you would go about implementing your proposed solution. What are key interfaces? What parts need to be done first? What things do you think will need the most careful testing?

I would really appreciate typed, double spaced and READABLE output that is firmly attached together. Sketches can of course be hand drawn. I am not looking for beauty, just legibility and room to mark them up. Generous margins are also nice.

PROBLEM 2

For the planar manipulator described in class, assume that the link lengths $a_i$ are subject to uncertainties $\Delta a_i$ and that the angles $\theta_i$ are subject to uncertainties $\Delta \theta_i$. Work out a formula for $[\Delta \bfR , \Delta \bfp]$

for this robot.\\[0.5in]

I would really appreciate typed, double spaced and READABLE output that is firmly attached together. However, don't worry if you want to hand-write this one (assuming readability) and don't want to hassle a formula formatter.

Sketches can of course be hand drawn. I am not looking for beauty, just legibility and room to mark them up. Generous margins are also nice.

EXERCISE PROBLEM: (early warning for subsequent assignments):}

Implement a small library for the following:

vector, rotation, frame transformation data types operations