Lecture 4 - Kinematics

Question 1

Translational velocity

Answer 1

rate of change of a point’s location

Question 2

A change of location is called…

Answer 2

translational motion / linear motion

Question 3

Translational velocity is a ___ (define) while speed is a ____ (define)

Answer 3

1. vector (size & direction) 2. number (size of velocity vector)

Question 4

simultaneous velocity combine by…

Answer 4

vector addition

Question 5

define: simultaneous velocity

Answer 5

velocities that happen at the same time (e.g. elbow and hand both move)

Question 6

2 types of motion that rigid bodies undergo

Answer 6

1. translation 2. rotation

Question 7

define: translation (pure translation)

Answer 7

change the body’s location (pure translation shifts every point in the body by the same vector)

Question 8

define: rotation

Answer 8

changes the body’s orientation

Question 9

how to specify rotation?

Answer 9

1. angle 2. direction about its axis

Question 10

How many DOF does rotation have? How is this split up?

Answer 10

3 DOF

• 1 specifies angle
• 2 specific axis (point on a sphere)

Question 11

How many DOF does translational motion have?

Answer 11

3 DOF

Question 12

translation is ____ but rotation is ____

Answer 12

intuitive; not

Question 13

Translational & rotational motion has the same DOF only because…

Answer 13

we are in 3D space

• In 4D, translation ahsa 4 DOF while rotational has 6 DOF

Question 14

define: non-commutative

Answer 14

order matters

Question 15

Is rotational motion commutative or non-commutative?

Answer 15

non-commutative

Question 16

To keep visual image stable, eye motion must depend on the…

Answer 16

order of body rotations

Question 17

does the VOR work commutatively or non-commutatively?

Answer 17

non-commutatively

Question 18

The operations in the neural circuits of the VOR mirrors the properties of _______. The brain performs _____ algebra

Answer 18

eye and head rotations;

non-commutative

Question 19

Rotational velocity is a ___ vector

Answer 19

3D

Question 20

At any instant, a spinning body has a unique…

Answer 20

axis of rotation

Question 21

define: rotational velocity

Answer 21

vector lying along the axis spin, with length equal to the rate of spin in radians/sec

Question 22

define: rotational speed

Answer 22

size of the rotational velocity vector

Question 23

How do we find the rotational velocity vector?

Answer 23

right hand rule (fingers follow rotation direction, thumb will point the direction of the vector)

Question 24

Rotational velocities combine by…

Answer 24

vector addition

Question 25

Even though sequential rotations combine ______, simultaneous rotational velocities combine ____ by _____

Answer 25

non-commutatively;

commutatively;

vector addition

Question 26

How is rotational motion described?

Answer 26

Yaw: no

Pitch: yes

Roll: ear to shoulder

Question 27

How does the brain create translation (e.g. move hand at a particular velocity or to target location)

Answer 27

use rotation (arm joints are rotary)

Question 28

How do different points on a rigid body translate?

Answer 28

translates differently

Question 29

How to calculate the translational velocity of point P on body B if we know point O, v_o, and w (rotational velocity of B)

Answer 29

v_p = v_o + w x (p - o)

Cross product