Upcoming Deadlines Ninth Homework (Stop-motion Character Animation) Due Tuesday, October 30 th (In two weeks) 20 points (10 points if late) Tenth Homework (Outline of Second Term Paper) Due Tuesday, November 6 th (In 3 weeks) 10 points (5 points if late) For full schedule, visit course website: Have clicker ready

Extra Credit Opportunities Cartoon Art Museum Mill Valley Film Festival Walt Disney Family Museum Exploratorium The Tech Museum (Mythbusters) Visit course website for more info. Extra credit opportunities:

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.

Homework Assignment #9

Homework Assignment #9 Post your animation clip to your blog in an entry entitled “Stop-Motion Character Animation.” As before, describe how you created it. Assignment is due by 8am on Tuesday, October 30 th 20 points (if late, 10 points) The top three clips in the class, as selected by another celebrity judge, receive a bonus of 20 extra points.

Anonymous Survey Results Likes: Demos, Videos, Clickers, Website, Organization Dislikes: Not enough math; Too much math Suggestions: More material (including online lectures); More advanced material; Discuss use of physics in the studios

Survey Question The amount (and the level) of mathematics in the class is: A)Too much math B)About right C)Too little math

Review Question If a giant walks with a gait that matches his size, would you walk at a faster speed than the giant? A)Yes, the giant has a slow, lumbering walk so you easily walk faster than him. B)No, because his gait matches his size you and the giant walk at the same speed. C)No, the giant walks faster than you do. Jason and the Argonauts

Cadence and Walking Speed C) No, the giant walks faster than you do. Legs x4 longer have x½ the cadence but x2 walking speed since x4 step length. x1 Distance x4 Time x2

Review Question In a normal walk, the timing going from the contact pose to the passing position is: A)Slowing out (Accelerating) B)Slowing in (Deceleration) C)Uniform motion

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

Review Question At which position do you exert the most total weight on the ground? A)Contact B)Squash C)Passing Position D)Stretch E)Same weight at all times Contact P.P. Squash Stretch

Weight Shift in Contact Pose Left foot Right foot A) Contact Body Weight

Weight Shift in Contact Pose Left foot Right foot Heel strike The weight on the back foot peaks just as the heel of the front foot touches the ground. Body Weight Falling & Slowing Down: Gain Weight

Weight Shift in Contact Pose Left foot Right foot Toe off Moments later, the weight on the front foot is peaked just as the back foot leaves the ground. Body Weight Rising & Speeding Up: Gain Weight

Walks Part II

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

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

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

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 = 0 P = 100 F = 0 K = 20 P = 70 F = 10 K = 40 P = 40 F = 20 Total Energy = 100

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

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.

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

Energy and Wile E. Coyote 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! From Going, Going, Gosh

Energy Budget (Animate) Animate objects can increase their energy budget by doing work. Work Input (W) – Energy added by doing work. K = 0 P = 0 F = 0 W = +0 Kinetic Energy Potential Energy Friction Losses Work Input K = 100 P = 0 F = 10 W = +110 K = 300 P = 0 F = 20 W = +320

Energy Budget in Jumping K = 0 P = 50 F = 0 W = 0 K = 200 P = 150 F = 50 W = +350 K = 120 P = 225 F = 55 W = +350 K = 90 P = 250 F = 60 W = +350 Leg muscles do work as you push off when jumping. Slow down as you rise to apex so kinetic energy (K) goes down. Most of the friction loss is during push but a little loss due to air resistance.

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

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.

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. CG Passing Position Contact Pose Passing Position Walking Forward We have to do work to raise the CG and much of that energy (30-40%) is lost to friction. Contact Pose

Simplified Walking Model CG

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

Pelvic Rotation & Center of Gravity Pelvic rotation keeps the center of gravity from dropping as far in the contact pose while keeping the step length the same. CG without pelvic rotation CG with pelvic rotation

Pelvic List for the Passing Leg 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.

Pelvic List for the Passing Leg 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. Contact Pose Passing Position Walking Forward Contact Pose CG without pelvic list CG with pelvic list

Knee Flexion for the Weighted Leg Knee flexes about 15 degrees just after the heel strike and remains flexed until the center of gravity passes over the weight bearing leg. Knee flexion keeps the center of gravity from rising as much during the passing position. Walking Forward Contact Pose Passing Position Contact Pose Passing Position CG without flexion CG with flexion

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. Heel increases effective length of the leg Flexion reduces the leg length Toes increase leg length Contact Pose Passing Position Contact Pose

Stride Width Shifting the center of gravity from left to right also requires work so a narrow stride is more efficient. Less Efficient More Efficient

Swaying Center of gravity moves both up-and-down and side-to-side, making an  -shaped loop when walking slow and a U-shape loop when walking fast. 85 steps per minute 120 steps per minute SlowFast SlowFast

8-Loop & U-Loop 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. Slow Fast Side-to-Side Up & Down Walking Forward Figure 8 Loop

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

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

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. Move Raise X CG Energy & Step Length

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

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

Quadruped Animal Walking Walking for animals is very different than for humans, not so much because they walk on 4 legs but due to bone structure.

101 Dalmations (1961) The walking gaits of the dogs in this scene is modified to match that of their masters. Walk cycles animated by Frank Thomas and Blaine Gibson Click

Shoulder, Elbow, Wrist Front legs of mammals have the same joints and bones as our arms but with varying lengths. From Chuck Amuck: The Life and Times of an Animated Cartoonist By Chuck Jones Shoulder Elbow Wrist Horse Human Dog Cat ???

Dog Legs Notice the joints circled in this skeleton of a dog; on a human these would be: A)Elbows and Knees B)Elbows and Ankles C)Wrists and Knees D)Wrists and Ankles E)None of the above

B) Elbows and Ankles Dog Legs

AT-AT Walkers Industrial Light & Magic (ILM) filmed the AT-ATs using stop-motion animation with models from 2 inches to 2 feet in height. Walking mimics elephants Star Wars Episode V: The Empire Strikes Back

Tennis Shoes & Stripped Socks From Chuck Amuck: The Life and Times of an Animated Cartoonist By Chuck Jones Chuck Jones presents a good way to remember animal anatomy: Tennis shoes & Stripped socks. Knee Ankle Sole

Sole, Ankle, Knee From Chuck Amuck: The Life and Times of an Animated Cartoonist By Chuck Jones Knee Ankle Sole Knee Ankle Sole Horse Human Dog What you think is the “knee” on the animal’s hind leg is actually the ankle.

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

Next Lecture Levers and Joints Next Assignment Stop-motion Character Animation Due Tue., Oct. 30 th (In 2 weeks)