Lecture 4 - Kinematics Flashcards
Translational velocity
rate of change of a point’s location
A change of location is called…
translational motion / linear motion
Translational velocity is a ___ (define) while speed is a ____ (define)
- vector (size & direction) 2. number (size of velocity vector)
simultaneous velocity combine by…
vector addition
define: simultaneous velocity
velocities that happen at the same time (e.g. elbow and hand both move)
2 types of motion that rigid bodies undergo
- translation 2. rotation
define: translation (pure translation)
change the body’s location (pure translation shifts every point in the body by the same vector)
define: rotation
changes the body’s orientation
how to specify rotation?
- angle 2. direction about its axis
How many DOF does rotation have? How is this split up?
3 DOF
- 1 specifies angle
- 2 specific axis (point on a sphere)
How many DOF does translational motion have?
3 DOF
translation is ____ but rotation is ____
intuitive; not
Translational & rotational motion has the same DOF only because…
we are in 3D space
- In 4D, translation ahsa 4 DOF while rotational has 6 DOF
define: non-commutative
order matters
Is rotational motion commutative or non-commutative?
non-commutative
To keep visual image stable, eye motion must depend on the…
order of body rotations
does the VOR work commutatively or non-commutatively?
non-commutatively
The operations in the neural circuits of the VOR mirrors the properties of _______. The brain performs _____ algebra
eye and head rotations;
non-commutative
Rotational velocity is a ___ vector
3D
At any instant, a spinning body has a unique…
axis of rotation
define: rotational velocity
vector lying along the axis spin, with length equal to the rate of spin in radians/sec
define: rotational speed
size of the rotational velocity vector
How do we find the rotational velocity vector?
right hand rule (fingers follow rotation direction, thumb will point the direction of the vector)
Rotational velocities combine by…
vector addition
Even though sequential rotations combine ______, simultaneous rotational velocities combine ____ by _____
non-commutatively;
commutatively;
vector addition
How is rotational motion described?
Yaw: no
Pitch: yes
Roll: ear to shoulder
How does the brain create translation (e.g. move hand at a particular velocity or to target location)
use rotation (arm joints are rotary)
How do different points on a rigid body translate?
translates differently
How to calculate the translational velocity of point P on body B if we know point O, vo, and w (rotational velocity of B)
vp = vo + w x (p - o)
Cross product
