TAM 7960
Legged Locomotion of Robots and Animals
(Terrestrial Locomotion)
Spring 2010
Updated March 5, 2010
Homework
Each homework assignment will start on a fresh page.
This document will grow in length as the
semester progresses.
HW due Tuesday Feb 2
1. A natural measure of energy use is ”The specific energetic cost of transport”,
Energy used
weight
distance
Note that weight is a force (mass times
) so
is a dimensionless number. Estimate, using
whatever numbers you know or look up, the
for at least 3 of these things.
a person walking
a person biking
a car (full weight)
a car (only counting weight of passengers)
a freight truck
a freight train
a passenger train (only counting weight of passengers)
some other animal of your choice, walking, running or flying.
Make your assumptions clear and clearly identify (so I can check) any sources you use. Best if
you have two different estimates, based on different types of data.
2. What would be a good measure of locomotion speed for comparing different animals or robots?
Justify your answer as best you can. If you have more than one candidate, compare them. I am
not looking for a quote from some paper or other, but your own thoughts.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
HW due Thursday Feb 11
1. An ideal passive transmission conserves energy. One example of a transmission is a screw
drive or ‘worm drive’ (read about such in, say, wikipedia). A model for the basic mechanics of
a worm drive (left) is the wedge (right).
A
B
F
A
F
B
F
A
F
B
F
A
N
A
N
B
F
B
F
F
A
B
ˆ
ı
ˆ
j
θ
θ
θ
(a)
(b)
(c)
(a) For simplicity, assume that all sliding is frictionless and that the parts have no mass or
weight. Think of A as the input and B as the output.
i. Find
in terms of
and
.
ii. From geometry (kinematics), find the sideways motion of B in terms of
and the
motion of A.
iii. Note that the results above are consistent with energy conservation.
iv. Simplify all of the expressions above using a small angle approximation (
sin
etc.
(b) Now include friction, but just on the surface AB. Assume a friction coefficient
or friction
angle
with tan
. Assume that the friction against the walls is still zero. For the
worm drive this is like assuming that the shafts have good bearings but that all the friction
is on the screw surface. Assume the wedge is going down.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Wilczynski
 Force, Mass, Angular velocity, average forward speed

Click to edit the document details