KINS 4200 Exam 2 Angular Kinematics

kinematics

movement of an object without regard to forces causing the motion

MOVEMENT

angular motion

motion around an axis of rotation

axis can be

moving or fixed

internal or external

in the body, usually talking about an axis that is

moving and internal

linear motion

all parts have same linear displacement

angular motion

all parts do NOT have the same linear displacement but DO have the same angular displacement

linear vs angular displacement example

person swinging leg

linear displacement of knee does not equal displacement of ankle

but angular displacement is the same

2D angles

intersection of two liens or places, orientation of a line in a plane

3D angles

orientation of a rigid body in space

units of measurement of angles

degrees, radians, revolutions

radian

angle at the center of a circle where an arc (s) equal to the length of the radius

ration of the distance around thh arc of the radius of the circle

to convert from degrees to radians

degrees x (π / 100) = radians

revolution

1 revolution = 2π radians = 360°

goniometer

tool used t measure the angle and range of motion of a body joint in degrees

absolute angle

angle of inclination of body segment relative to some fixed reference

orientation of segment in space

typically aligned to right horizontal

relative angle

segment movement described relative to the adjacent segment

angle between two body segments

computing absolute angles

θ = tan⁻¹ (( Y_prox - Y _dist) / (X_prox - X _dist))

+x +y angle relative to horizontal

leave answer alone

-x +y angle relative to horizontal

add 180 to find answer

-x -y absolute angle relative to horizontal

add 180 to find answer

+x -y absolute angle relative to the right horizontal

add 360 to find answer

ex. how to find knee angle

θ _knee = θ _thigh - θ _leg

computing relative angles

θ = cos⁻¹ ( (b² + c² - a²) / (2bc) )

steps of computing relative angle

when trying to solve for the θ of the knee

1. must calculate the lines of the triangle using √( (X_b - X_a )² + (Y_b - Y_a)²

2. then use each of those lines and input them into 2nd formula

cons to computing relative angles

does not describe position of segments or angles in space

ex. 90* elbow angle can be in any number of positions

angular position

an objects position relative to a defined spatial reference system

angular displacement

change in angular position

θ = θ_final - θ_initial

angular velocity

change in angular position / change in time

units: degrees/second or radians/second

angular acceleration

change in angular velocity / change in time

units: degrees/second² or radians/second²

first finite central difference method

use information directly after and before to find information

linear and angular displacement of human movement

motions of body segments are angular by produce resulting linear movement

angular displacement change with radius

despite difference in radius of rotation, angular displacement does nto change, but linear displacement does change

linear displacement formula

radius of rotation x angular displacement

△S = r x △θ

linear displacement as a result of angular motion is only valid IF:

θ is calculated in radians

tangential velocity

linear motion resulting from angular motion

velocity is tangent to the path of an object

units: m/s

only valid if calculaed in rad/sec

how to maximize tangential velocity

increase either radius of rotation or angular velocity to increase tangential velocity

tangential acceleration

acceleration direction is at a tangent to the curved path

only valid if calculated in rad/sec²

tangential acceleration formula

a_t = r x a

r = radius of rotation

a = angular acceleration

centripetal acceleration

component of angular acceleration directed toward the center of curvature than indicates change in direction

always directed inward, toward teh center of a curved path

tighter turning radius =

= greater centripetal acceleration

hip extended the most during

50% point of gait cycle

knee flexed the most during

75% point of gait cycle

ankle is plantar flexed then most during

63% point during gait cycle

ankle is dorsi flexed the most during

50% of gait cycle