1. Upcoming Deadlines Spring Break - March 26th to March 30th
Pick up a clicker, find the right channel, and enter Student ID
Spring Break - March 26th to March 30th
Ninth Homework (Stop-motion Character Animation)
Due by 8am on Tuesday, April 10th
20 points (10 points if late)
For full schedule, visit course website:
ArtPhysics123.pbworks.com

2. Extra Credit Opportunity
Attend any event at 55th San Francisco International Film Festival, April 19–May 3, in San Francisco.
Present proof of you attendance (receipt, photos, etc.) for 10 points of extra credit.

3. Homework Assignment #9
In this assignment you will create a simple stop-motion animation of a moving character.
For your character, use a doll or stuffed animal that's easily posed.
You may even use an inanimate object, such as a table lamp, as long as you can animate it so that it looks like a character.

4. Homework Assignment #9

5. Homework Assignment #9
Your animation should be composed of at least a dozen different images but you can use the same photo in two or more frames to get timing right. Try to make the motion of the character as realistic as possible so that your audience will momentarily forget that it's not actually alive. In homework assignment #6 you created a stop-motion animation of an inanimate falling object; if you're not happy with how you produced your earlier animation then re-read that assignment for alternative ways of creating stop-motion.

6. Homework Assignment #9
You may work together with one or more classmates to create a single animation for the team. Clearly indicate the work done by each person, for example if different persons animate different characters or different scenes. More is expected from a team effort; an animation created by a three person team should present three times as much work as a solo effort.

7. Homework Assignment #9 Assignment is due by 8am on Tuesday, April 10th
Post your animation clip to your blog in an entry entitled "Stop-Motion Character Animation.“
Assignment is due by 8am on Tuesday, April 10th
20 points (if late, 10 points)
The top three clips in the class, as selected by another celebrity judge, will receive a bonus of 20 extra points.

8. Survey Question
How often have you gone to the course website to look at the lecture slides?
More than 10 times
About 5 to 10 times
A couple of times
Never

9. Review Question
In a normal walk, the timing going from the stride to the passing position is:
Slowing out (Accelerating)
Slowing in (Deceleration)
Uniform motion

10. Rolling Egg Timing B) Slowing In (Decelerating)
Slowing Out
XCG
The timing of the motion due rising and falling center of gravity (CG) is like that of a rolling egg.

11. Review Question
Stride
Squash
Passing Position
Stretch
Same weight at all times
At which position do you exert the least weight on the ground?
P.P.
Stretch
Stretch
Stride
P.P.
Stride
Stride
Squash
Squash

12. Force Plate Experiments
Upward centrifugal force due to your motion lightens your weight.
Stride
C) Passing Position
Can measure weight shift during walk cycle using force plates.
Squash
Squash
Stretch
Stretch
Body Weight
Passing
Position
Passing
Position

13. Walks Part II

14. Ray Harryhausen
Ray Harryhausen, the master of stop-motion animation, created the special effects in many films from the 1940’s to the 1970’s
One of his best scenes in the skeleton battle in Jason and the Argonauts

15. Skeleton Battle Scene
Notice how the animated skeletons walk (conveniently, we see their pelvis and leg bones).

16. Energy and Walking
So far we’ve examined walking from the point of view of forces.
An alternative approach is to examine the energy expended in walking.
We’re inherently lazy so many actions that we perform unconsciously while walking reduce energy expenditure.

17. Energy Budget (Inanimate)
Moving objects have an energy budget.
For inanimate objects, this budget is:
Kinetic Energy (K) – Energy due to their speed
Potential Energy (P) – Energy due to their height
Friction Loss (F) – Energy lost due to friction forces
K = 40
P = 40
F = 20
K = 0
P = 100
F = 0
K = 20
P = 70
F = 10
Total Energy = 100

18. Demo: Ball Races
Marbles start at equal height and race on these rail tracks (almost no friction).
Track B has a long dip in the center.
Winner? A) Ball A; B) Ball B; C) Near perfect tie.
Hint: Kinetic energy + Potential energy stays constant.

19. Demo: Ball Races B) Ball B is the winner.
K = 50
P = 50
F = 0
K = 50
P = 50
F = 0
K = 50
P = 50
F = 0
K = 0
P = 100
F = 0
K = 50
P = 50
F = 0
K = 50
P = 50
F = 0
K = 100
P = 0
F = 0
Ball B has a high speed in the center section.

20. Energy and Wile E. Coyote
From Going, Going, Gosh
The energy budget here is wrong because the rock, after rolling down hill, flies back up to a point higher than from where it started!

21. Energy Budget, Bouncing
Kinetic Energy
Potential Energy
Friction Losses
K = 45
P = 5
F = 0
K = 36
P = 4
F = 10
K = 50
P = 0
F = 0
Total Energy = 50

22. Energy Budget, Sack Drop
F = 0
Flour sack sitting on a shelf starts with potential energy.
After it settles, all the energy is lost to friction forces.
What is the kinetic energy when fallen half-way down?
K = ???
P = 100
F = 5
(Air resistance)
Zero
200
100 95
105
K = 0
P =
F = 200
Kinetic Energy
Potential Energy
Friction Losses

23. Energy Budget, Sack Drop
The total budget (K+P+F) has to equal 200.
If there was no air resistance then the falling speed would be greater and K=100.
With more air resistance, the friction loss would be greater and kinetic energy less.
K = 0
P = 200
F = 0
K = 95
P = 100
F = 5
(Air resistance)
K = 0
P =
F = 200
Kinetic Energy
Potential Energy
Friction Losses

24. Energy Budget (Animate)
Animate objects can increase their energy budget by doing work.
Work Input (W) – Energy added by doing work.
Kinetic Energy
Potential Energy
Friction Losses
Work Input
K =
P =
F =
W = +0
K =
P =
F =
W = +110
K =
P =
F =
W = +320

25. Energy Budget in Jumping
Slow down as you rise to apex so kinetic energy (K) goes down.
K = 0
P = 50
F = 0 W = 0
K = 200
P = 100
F = 50 W = +350
K = 120
P = 175
F = 55 W = +350
K = 90
P = 200
F = 60 W = +350
Leg muscles do work as you push off when jumping.
Most of the friction loss is during push but a little loss due to air resistance.

26. Energy Budget in Walking
P = 100
F = 0 W = +0
K = 100
P = 100
F = 60 W = +60
Walking takes work due to all the frictional losses.

27. Home Demo: Silly Walks
Try walking around as John Cleese, who is the Minister of Silly Walks.
You will find that you use much more energy than normal walking.

28. Simplified Walking Model
Pelvis is a double-forked bar with spherical hip joints. Legs are straight bars without knees, ankles, or feet.
Center of gravity rises and falls as an inverted pendulum.
Walking Forward CG
Passing Position
Stride CG
Passing Position
Stride
Passing Position
We have to do work to raise the CG and much of that energy (30-40%) is lost to friction.

29. Simplified Walking Model
Pelvis is a double-forked bar with spherical hip joints. Legs are straight bars without knees, ankles, or feet.
Center of gravity rises and falls as an inverted pendulum.
Walking Forward CG
Passing Position
Stride CG
Passing Position
Stride
Passing Position
We have to do work to raise the CG and much of that energy (30-40%) is lost to friction.

30. Simplified Walking Model

31. Pelvic Rotation
Without
Rotation
As the passing leg swings forward, the hips swing around, rotating about the planted leg.
With
Rotation

32. Pelvic Rotation

33. Pelvic Rotation & Center of Gravity
Pelvic rotation keeps the center of gravity from dropping as far during the stride (keeping step length the same). CG
Path of Action of CG with Rotation
Without Rotation
Passing Position
Stride CG
Walking Forward
Stride
Passing Position
Passing Position
Walking is more efficient with pelvic rotation.

34. Pelvic List
In the passing position the pelvis drops slightly on the non-weight bearing side. This motion is called “pelvic list.”
Note that the knee has to bend to lift the foot, otherwise it would drag the ground.

35. Pelvic List

36. Pelvic List & Center of GravityCG
Path of Action of CG without List
Pelvic list keeps the center of gravity from rising as much when the body passes over the weight-bearing leg, keeping the center of gravity on a flatter path of action.
With Pelvic List
Passing Position
Stride CG
Walking Forward
Passing Position
Stride
Passing Position
Walking is more efficient with pelvic list.

37. Knee Flexion of Weighted Leg
Knee flexes about 15 degrees immediately after heel strike and remains flexed until the center of gravity passes over the weight bearing leg.
Walking Forward

38. Knee Flexion of Weighted Leg

39. Knee Flexion
Path of Action of CG without Flexion CG
Knee flexion keeps the center of gravity from rising as much during the passing position. Knee flexion also reduces the impact on the body at heel strike.
With Flexion
Passing Position
Stride CG
Walking Forward
Passing Position
Stride
Passing Position
Walking is more efficient with knee flexion.

40. Heel and Toe
The heel and toes of the foot combine with knee flexion to reduce the rising and falling of the center of gravity.
Flexion reduces the leg length
Toes increase leg length
Heel increases effective length of the leg

41. Energy in Four-legged Walks
Four-legged walking gait alternates passing position and stride between fore and hind legs to minimize energy required to lift the center of gravity.
Height x
Center of Gravity
The Journal of Experimental Biology 207, (2004)

42. Stride Width
Shifting the center of gravity from left to right requires work so a wide stride is less efficient.
Less
Efficient
More
Efficient

43. 8-Loop & U-Loop
Side-to-Side
The center of gravity shifts up & down but also side-to-side.
CG makes a Figure-8 loop when walking slow Makes a U-shape loop when walking fast.
Up & Down
Figure 8 Loop
Walking Forward
Slow
Fast

44. Look (2009)
This music video is one long walk cycle, focusing on the motion of the hips.

45. Step Length When walking, why don’t we take longer (or shorter) steps?
We naturally adjust our step length to minimize the energy output required to maintain our desired walking speed.
Step length

46. Energy & Step Length Energy is required to:
Move the leg forward in the stride; longer steps take less energy.
Raise the body in the passing position; longer steps take more energy.
Raise
XCG
XCG
Move

47. Optimum Step Length
Longer Steps, Slower Cadence
Shorter Steps, Quicker Cadence
Treadmill data of metabolic rate while walking at 2½ mph
Optimum Step Length
Work done per minute
Step Length (meters)
The body adjusts the step length to minimize the total energy expended while maintaining desired speed.

48. Energetic Walks
A character with lots of energy will have a walk that doesn’t try to minimize the up/down motion.
Various walks by Preston Blair

49. Shoulder Rotation
The shoulders rotate opposite from the hips, swinging over the planted leg.

50. Arm Swing
The arm swings back and forth, also like a pendulum, roughly 180o out of phase with the leg.
The arm and leg are roughly the same length so they swing back and forth with about the same period.

51. Who Framed Roger Rabbit? (1988)
Notice the complementary, counter-rotating motion of Jessica’s upper and lower body.

52. Video Analysis of Arm & Leg

53. Hand and Ankle
Hand and ankle on opposite sides follow similar triangular or half-teardrop pattern.

54. Richard Williams’ ASK
Williams shows a similar half-teardrop path of action in the motion of the ankle.

55. Rotation Balance
Moving your legs (and hips) as you walk requires a torque (rotational force) to turn them.
It takes less effort if you balance the rotation of the lower body with
an opposite rotation of your upper body.
Katie Corna

56. Demo: The Twist
Try dancing The Twist in the normal way, moving the hips opposite from the shoulders.
Then try to dance it the wrong way, moving hips and shoulders together, back and forth.

57. Next Lecture Levers and Joints
Enjoy Spring Break!
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