Upcoming Deadlines

Homework #9 – Stop-motion character AnimationDue 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

Pick up a clicker, find the right channel, and enter Student ID

Survey QuestionMany videos are shown in this class;

would you say that the number of videos is:

A) Too many. Use the class time for other stuff.

B) About the right balance.C) Not enough. Add more and leave out

other stuff.

Review QuestionIn the passing position the pelvis drops slightly on the non-weight bearing side. This motion is called:A) Pelvic rotationB) Pelvic listC) Knee flexionD)Hip hula-hulaE) The Twist

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.

CG

Stride

Passing Position

Passing Position

Passing Position

Stride

CG

Walking is more efficient with pelvic list.

Path of Action ofCG without List

With Pelvic List

Walking Fo

rward

B) Pelvic list

Stride WidthShifting the center of gravity from left to right requires work so a wide stride is less efficient.

LessEfficient

MoreEfficient

8-Loop & U-LoopThe 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 8Loop

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

http://www.youtube.com/watch?v=KX82DXvmQu4

Step LengthWhen 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

XCGXCG

Energy & Step Length

Optimum Step Length

Wor

k do

ne p

er m

inut

e

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.

Shoulder RotationThe shoulders rotate opposite from the hips, swinging over the planted leg.

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.

Hand and Ankle

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

Richard Williams’ ASK

Williams shows a similar half-teardrop path of action in the motion of the ankle.

Rotation Balance

It takes less effort if you balance the rotation of the lower body with an opposite rotation of your upper body.

Moving your legs (and hips) as you walk requires a torque (rotational force) to turn them.

Katie Corna

Demo: The TwistTry 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

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.

Realism

Appe

al

Emily Project

PolarExpress

Shrek 1

Beowulf

Toy Story

Tin Toy

http://www.youtube.com/

watch?v=GBgURIUQ700

“Realism Tightrope”The uncanny valley occurs when some elements are more realistic than others.

Our human instincts warn us something is wrong.

Realistic Image

Appe

al

Realistic Motion

Completely Natural

Tolerable

Repulsive

Repulsive

Robot Zombie

Tolerable

Articulated FiguresIn 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

Revolute Joint Prismatic Joint (Slider)

Two kinds of joints: Revolute (rotation) and Prismatic (extension/contraction).

Nearly all joints in animals are revolute joints

Axis of RotationRotation occurs around a line called

the axis of rotation.The axle is the axis of rotation for a set of wheels.

Revolute JointsRevolute 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.

Elbow

Shoulder

Forearm

Forward KineticsWith 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 KineticsForward 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 KineticsWith inverse kinetics (IK) the animator positions the end effector, such as the hand, and the computer calculates the required joint rotations.

Inverse KineticsRotations calculated by the computer using IK are not always natural poses performed by a person. Furthermore, the timing may not be correct.

Ball & Socket

Ball & Socket

Hinge

x

x

Raising hand into “High Five” pose

AwkwardIK Pose

Elbow

Wrist

Shoulder

Understanding RotationJust 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

Mass is a measure of inertia for linear motion.

Rotational inertia is similar concept for rotation.

Inertia

M mGold brick Normal brick

Difficult to move Easy to move

x xWood Bat Plastic Pee-wee Bat

Difficult to Rotate Easy to Rotate

Rotational InertiaRotational 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 SticksTwo metal pipes of the same mass

Rotate

Leadweights

Easyto

Rotate

Hardto

Rotate

Axis ofRotation

Human Rotational InertiaIn which pose does the dancer have a

larger rotational inertia?Axis of Rotation

A B

A) Pose AB) Pose BC) Same for A & B

since mass is unchanged.

Human Rotational Inertia

Axis of Rotation

A B

B) Pose B

Pose B has larger rotational inertia since the leg is extended, putting mass further from the axis of rotation.

Demo: Long LegsLong legs have greater

rotational inertia than short legs so long legged animals have a slow walking stride.

Drag of Articulated Limbs

Fast Swing

Slow SwingSlow

Fast

The greater rotational inertia of longer limbs results in “drag”, just like with hair and fabrics.

Demo: Drop the StickTwo 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

Axis of Rotation

X CG

X CG

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.

Longer stick tips over more slowly

Tripping and Falling

Axis of Rotation

X CG

X CG

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.

Demo: Hammer Balance

BA

Axis of Rotation

In which case is the hammer easier to balance on your finger?

A) Case AB) Case BC) The same for A & B

Demo: Hammer BalanceB) Case BIn 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).

BA

X CG

X CG