Angular Kinematics

Angular motion

motion around an axis of rotation; ex: spins, swings, or twists

Radians

ratio between the length of an arc and its radius in a given circle, rad = arc length/ radius.

Degrees to radian

degrees/57.3= rad

radians to degrees

57.3 x rad = degrees

Absolute angles

angle between a segment and the right horizontal of the distal end, measure angle from horizontal line in a ccw direction

Relative angles

joint angles, angle between the longitudinal axis of two adjacent segments; fully extended position is defined as either 0 or 180 degrees.

Relative angle of a hip joint

flexion: +

extension:-

relative angle of a knee joint

flexion:+

extension:-

relative angle of an ankle joint

dorsiflexion:+

plantarflexion:-

Calculating absolute angles

θ = 𝐭𝐚𝐧−𝟏(y proximal – y distal/ x proximal – x distal )

Absolute angle quadrant 1

+x, +y

Absolute angle quadrant 2

-x, +y, add 180 degrees to absolute angle

Absolute angle quadrant 3

-x, -y, add 180 to absolute angle

Absolute angle quadrant 4

+x, -y, add 360 to absolute angle

Law of Cosines

used if you have segment lengths, or points for three joints; 1st calculate the length of each side then calculate the cosine theta angle.

Two absolute angles

find relative angles using absolute angles, θrelative= 𝛉 absolute leg + (180 - 𝛉absolute thigh)

Relative angle hip

𝛉Hip = θ trunk +(180 −θthigh)

Relative angle knee

𝛉𝐊𝐧𝐞𝐞 =θshank + (180 −θthigh)

Relative angle of ankle

𝛉Ankle = θ shank + (180 – θ foot)