Upcoming Deadlines Pick up a clicker, find the right channel, and enter Student ID Homework #9 – Stop-motion character Animation Due Thursday, November 10th (Next week) 20 points (10 points if late); 20 point bonus to top 3 For full schedule, visit course website: ArtPhysics123.pbworks.com

Survey Question Many videos are shown in this class; would you say that the number of videos is: Too many. Use the class time for other stuff. About the right balance. Not enough. Add more and leave out other stuff.

Review Question In the passing position the pelvis drops slightly on the non-weight bearing side. This motion is called: Pelvic rotation Pelvic list Knee flexion Hip hula-hula The Twist

Pelvic List B) Pelvic list Walking is more efficient with pelvic list. CG Path of Action of CG without List B) Pelvic list With Pelvic 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. Passing Position Stride CG Walking Forward Passing Position Stride Passing Position Walking is more efficient with pelvic list.

Stride Width Shifting the center of gravity from left to right requires work so a wide stride is less efficient. Less Efficient More Efficient 5

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 6

Look (2009) This music video is one long walk cycle, focusing on the motion of the hips. http://www.youtube.com/watch?v=KX82DXvmQu4 7

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 8

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 9

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. 10

Shoulder Rotation The shoulders rotate opposite from the hips, swinging over the planted leg. 11

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. 12

Hand and Ankle Hand and ankle on opposite sides follow similar triangular or half-teardrop pattern. 13

Richard Williams’ ASK Williams shows a similar half-teardrop path of action in the motion of the ankle. 14

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 15

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. http://www.youtube.com/watch?v=8FTTFo6mcug 16

Joints & Levers

Toy Story (1995) Pixar’s Toy Story, directed by John Lasseter, was the first full-length feature film using computer animation. Tin Toy (1988, Pixar), also directed by Lasseter, won an Oscar in 1988 for Animated Short Film.

Tin Toy (1988) http://www.youtube.com/watch?v=vNZtl5SZvbM

The Polar Express (2004) The Polar Express was first full-length feature film made entirely with motion-capture animation. http://www.youtube.com/watch?v=2g-FRSq7x_o

“Uncanny Valley” Paradoxically, as computer generated characters get more realistic they start to be creepy. http://www.youtube.com/ watch?v=GBgURIUQ700 Toy Story Appeal  Shrek 1 Emily Project Tin Toy Realism  Polar Express Beowulf

“Realism Tightrope” Appeal  Completely Natural The uncanny valley occurs when some elements are more realistic than others. Our human instincts warn us something is wrong. Tolerable Tolerable Zombie Robot Appeal  Repulsive Repulsive  Realistic Motion Realistic Image 

Articulated Figures In computer animation characters are articulated figures, like marionette puppets. The challenge for animators is to move all the elements (arms, legs, hands, etc.) believably from frame to frame.

Joints Two kinds of joints: Revolute (rotation) and Prismatic (extension/contraction). Prismatic Joint (Slider) Revolute Joint Nearly all joints in animals are revolute joints

Axis of Rotation Rotation occurs around a line called the axis of rotation. The axle is the axis of rotation for a set of wheels.

Revolute Joints Revolute joints may have a single axis of rotation, like hinge joints and pivot joints, or a variable axis, such as the ball and socket joint. Forearm Shoulder Elbow

Forward Kinetics With forward kinetics (FK) the animator has to specify the axis of rotation and the angle of rotation for each joint on a moving limb. Lift the arm by a shoulder rotation Move forearm by an elbow rotation

Forward Kinetics Forward kinetics (FK) is a tedious process for the animator and it is difficult to maintain certain constraints, such as the planted foot in a walk.

Inverse Kinetics With inverse kinetics (IK) the animator positions the end effector, such as the hand, and the computer calculates the required joint rotations.

Inverse Kinetics Rotations calculated by the computer using IK are not always natural poses performed by a person. Furthermore, the timing may not be correct. Ball & Socket Shoulder x Awkward IK Pose Wrist Hinge Elbow Raising hand into “High Five” pose x Ball & Socket

Understanding Rotation Just like any other type of motion, rotation is governed by Newton’s laws: Law of Inertia Law of Acceleration Action-Reaction Principle Let’s see how inertia, force, reaction, etc. appear in the context of rotational motion. Sir Isaac Newton

Inertia Mass is a measure of inertia for linear motion. Rotational inertia is similar concept for rotation. Gold brick Normal brick M m Difficult to move Easy to move Wood Bat Plastic Pee-wee Bat x x Difficult to Rotate Easy to Rotate

Rotational Inertia Rotational inertia depends on: Total mass of the object How the mass is distributed The farther the object’s mass is from the axis of rotation, the larger the rotational inertia.

Demo: Inertia Sticks Two metal pipes of the same mass Easy to Rotate Hard Lead weights Rotate Axis of Rotation

Human Rotational Inertia In which pose does the dancer have a larger rotational inertia? Axis of Rotation Pose A Pose B Same for A & B since mass is unchanged. A B

Human Rotational Inertia B) Pose B Pose B has larger rotational inertia since the leg is extended, putting mass further from the axis of rotation. Axis of Rotation A B

Demo: Long Legs Long legs have greater rotational inertia than short legs so long legged animals have a slow walking stride.

Drag of Articulated Limbs The greater rotational inertia of longer limbs results in “drag”, just like with hair and fabrics. Fast Fast Swing Slow Slow Swing

Demo: Drop the Stick Two meter sticks stand upright against a wall; one has a hunk of clay on the end. Which stick will swing down and hit the floor first? The one without the hunk of clay. Why? Clay increases rotational inertia, which slows the rotation. Axis of Rotation

Demo: Drop the Stick Another way to understand why the weighted stick takes longer to fall is that it’s center of gravity is higher. The higher it is, the longer it takes for an object to fall to the ground. X CG X CG Longer stick tips over more slowly Axis of Rotation

Tripping and Falling If small child trips, he hits the ground more quickly than an adult. Can view this two ways: *Child has small rotational inertia. *Child’s center of gravity is initially closer to the ground. X CG X CG Axis of Rotation

Demo: Hammer Balance In which case is the hammer easier to balance on your finger? Case A Case B The same for A & B B A Axis of Rotation

Demo: Hammer Balance B) Case B In Case B the rotation is slower and thus easier to balance. In case B the rotational inertia is greater because most of the mass is far from the axis of rotation (at your fingertip). B A X CG X CG