Angular Position and Measurement

Angular Position

• Refers to the orientation of a line relative to another line or plane.
• Absolute angular position is when the other line or plane is fixed relative to the earth.
• The forearm angle relative to a horizontal plane is an example of absolute angular position because the horizontal plane is a fixed reference.
• Relative angular position is when the other line or plane can move.
• The forearm's angle relative to the upper arm describes the relative angular position, such as the elbow joint angle.
• Limb angles at joints describe relative angular positions, with anatomists using specific terms for limb positions and movements.

Units of Measurement for Angles

• Degrees are a common unit, but radians exist as well.
• To measure line AB's absolute angle with a horizontal plane, imagine a horizontal line BC of the same length.
• A circle can be drawn with the length of AB as the radius and point B as the center.
• The angle of ABC is a fraction of the circle made by the pie piece ABC.
• One degree (1°) represents 1/360 of a circle, because a circle contains 360°.
• Angles can also be described by measuring how many radii are in the arc length AC, given one radius equals the length of line segment BC or AB.

Angular Displacement

• It is the angular analog of linear displacement.
• It represents the change in absolute angular position experienced by a rotating line and is the angle between the final and initial positions of that rotating line.
• To measure the angular displacement of a non-linear object, select two points and imagine a line connecting them; if the object is rigid, the angular displacement of the line segment mirrors the object's angular displacement.
• An angle in radians is the ratio of arc length to radius.
• A radian (rad) is a unit of measure for an angle representing the ratio of arc length to the radius.
• One radian, pi radians, and 2*pi radians are all ways to refer to angles.
• Conversions include 2pi radians in a circle or 2pi radians in 360°.

Direction of Angular Displacement

• Like linear displacement, angular displacement has a direction.
• Common terms to describe the direction of rotation include clockwise and counterclockwise.
• Clock hands rotate clockwise when viewed from the front, but from the back, they appear to rotate counterclockwise due to the change in perspective.
• Describing angular displacement as clockwise necessitates knowing the viewing position.
• To avoid confusion, identify the axis of rotation and the plane in which the part rotates; the axis of rotation is always perpendicular to the plane of motion.
• The axis of rotation is like a bicycle wheel's axle, with the spokes in the plane of motion.
• Establish a positive direction along the axis of rotation by positioning the right hand's thumb in the positive direction along the axis of rotation and the direction the fingers curl indicating the positive direction of rotation, known as the "right-hand thumb rule".
• For clock hands, the plane of motion is the clock face, and the axis of rotation is a line through the clock face; if the positive direction is out of the clock face, the positive rotation direction is counterclockwise.
• Screws, nuts, and bolts typically have right-handed threads, following the right-hand thumb rule where the thumb points in the desired movement direction, and fingers curl in the turning direction.

Measuring Angular Displacement

• A pitcher's shoulder joint range of motion is measured by having the pitcher abduct their shoulder (raise their arm away from their side as far as possible).
• The axis of rotation is the anteroposterior axis, a line through the shoulder joint with the positive direction towards the observer, and the plane of motion is the frontal plane formed by the arms, legs, and trunk.
• If the arm's initial position is 5° from vertical and the final position is 170° from vertical, the angular displacement (Δθ) is calculated as the final position (θf) minus the initial position (θi): Δθ = θf - θi.
• For example:
  • Δθ = 170° - 5°
  • Δθ = +165°
• Where:
  • Δθ = angular displacement,
  • θf = final angular position,
  • θi = initial angular position.
• The displacement is positive because the rotation aligns with the direction the fingers curl when the right thumb points anteriorly away from the shoulder.
• While coaches or teachers may not measure angular displacements with precision, angular displacement is crucial in certain sports; twists or somersaults in diving, gymnastics, or figure skating, are all measures of angular displacement.

Angular and Linear Displacement

• Muscle attachments close to joints result in small moment arms and require large muscle forces to produce modest torques.
• The distance any point on the arm moves during flexion depends on its distance from the elbow.
• Measured in radians, angular displacement is arc length/radius.
• Since all points on the forearm undergo identical angular displacement (Δθ): l/r = Δθ = la/ra = lb/rb
• If you multiply both sides of the last two terms of the equation by ra and divide both sides by "l", it shows that the ratios of arc lengths moved by any two points on the forearm are equal to the ratios of their radii from the elbow joint (axis of rotation).
• The equation is: la/l = ra/r
• To solve this equation, with four variables, know three of them.
• For instance, if wrist is 10 in. (25 cm) from the elbow and we want to know how far the wrist moves when the biceps tendon insertion point moves through an arc length of 1 in. (2.5 cm), given this insertion point is 1 in. (2.5 cm) from the elbow joint by setting:
  • ra = 10 in. (25 cm),
  • r = 1 in. (2.5 cm), and
  • l = 1 in. (2.5 cm),
• Equation is used to describe the wrist movement.