Torque and Angle Relationship

Angular Kinetics

• The equation for torque is T = F • d1, so torque is typically measured in N•m and lb ft
• Counterclockwise torques are usually positive, while clockwise torques are negative
• Torque is equally determined by the size of the force and the moment arm
• Increase torque by increasing the applied force or effective moment arm

Increasing Moment Arm

• It’s often easier and faster than months of conditioning

Example: Therapist Testing Elbow Extensors

• A therapist can provide resistance with a dynamometer to manually test isometric strength
• The moment arm increases and the required force decreases when the therapist positions their arm more distally

Torque and Levers

• A lever makes a nearly rigid object rotate about an axis
• Levers magnify speed or force
• Most human body segment levers magnify speed because the moment arm for the effort is less than the moment arm for the resistance being moved
• A biceps brachii must make a large force to make a torque larger than the torque created by a dumbbell
• A small amount of muscle shortening creates greater rotation and speed at the hand

Optimizing Torque Output

• Thirty pounds of force times a 4-foot moment arm equals 120 lb.ft of torque
• Conventionally, counterclockwise torque is positive
• A smaller moment arm results in smaller torque and angular motion if force magnitude stays the same

Torque Measurement

• Joint torques can be measured using isokinetic dynamometers in exercise science

Isometric Joint Torques

• Peak torques of several muscle groups for males
• Examples: Trunk extension 258 N•m (190 lb.ft), Knee extension 204 N•m (150 lb.ft)
• The torque-angle graphs from isokinetic testing show multiple muscle mechanical variables

Factors Affecting Torque Production

• The angle of the joints
• Variations in moment arm
• Muscle angle of pull
• The force-length relationship of the muscle

Torque as a Muscular Strength Variable

• Expressing muscular strength through torque is useful because it’s independent of the force’s point of application to the limb
• Variations in pad placement do not affect the torque measured by an isokinetic machine for similar effort

Summing Torques

• An object's rotation depends on the balance of torques created by the forces acting on it
• Summing torques must take into account the vector nature of torques
• All muscles of a muscle group combine to create a joint torque in a specific direction
• Torques from antagonist muscles, ligaments, and external forces must be summed with muscle group torques
• (60 • 0.06 + 90 • 0.03 = 6.3 N•m) is the net torque from the anterior deltoid and long head of the biceps

Gravitational Torque Example

• If a person's arm weight creates a gravitational torque of -16 N•m and the muscle net torque, the resultant torque at the shoulder is -9.7 N•m

Muscle-Balance and Strength Curves

• Isokinetic dynamometer testing records strength curves (joint torque-angle graphs) of muscle groups
• Isokinetic testing provides normative torques and valuable information regarding the ratio of strength between opposing muscle groups
• Hip flexor peak torques tend to be 60-75% of peak hip extensor torques
• Peak concentric hamstring torque is typically 40-50% of peak concentric quadriceps torque, close to the physiological cross-sectional area difference

Factors Affecting Strength (Torque Capability)

• Testing equipment
• Protocol
• Body position

Calculating Resultant Torque

• Sum the gravitational torque (-16 N•m) and the net muscle torque (6.3 N•m) to find the resultant torque of -9.7 N•m
• The shoulder flexors act eccentrically to lower the arm creating an extension torque
• The force must be multiplied by the moment arm, before assigning the appropriate sign

Joint Torques

• Joint torques calculated from inverse dynamics often exceed those measured on isokinetic dynamometers
• Energy transfer from biarticular muscles, differences in muscle action, and coactivation explain this phenomenon
• Coactivation of opposing torques is illustrated by EMG research showing isokinetic joint torques underestimate net agonist muscle torque

Angular Inertia (Moment Of Inertia)

• Moment of force, or torque, makes rotation
• Angular motion’s mechanical resistance is measured by the moment of inertia
• Inertia and moment are used because it uses the terms from moment of force
• The moment of inertia, like mass (linear inertia), is angular acceleration resistance

Moment of Inertia

• An object has an infinite number of moments of inertia, although its mass is constant
• The object may be rotated about an infinite number of axes
• Rotating the human body is interesting because the links allow body configuration to change along with the axes of rotation

Symbol

• I is the symbol for the moment of inertia and subscripts denote rotational axis

Moment of Inertia Formula

• The rigid-body moment of inertia about an axis (A) is IA = _mr2
• Axis is cut into small masses of known radial distances from the axis
• Note that the SI units of moment of inertia are kg.m2

Distribution of Mass

• An object's resistance to rotation depends more on the distribution of mass (r2) than mass (m)
• Changes in location of mass relative to the axis of rotation increase moment of inertia
• Configurations of body segments change relative to the axis of rotation and manipulate the moment of inertia

Bending Joints

• Bending the joints of the upper and lower extremities brings segmental masses close to a rotation axis, reducing limb’s moment of inertia
• Easier angular acceleration and motion results
• Greater knee flexion helps the leg rotate and get into position for another footstrike
• Skilled gymnastic tumbling relies on decreasing human body moment of inertia to allow rotations
• Lengthening the body slows rotation down

Variations in Moment of Inertia

• Very important to performance
• A longer implement has a similar swing weight to a shorter implement by keeping mass proximal and using low mass for added length

Three-Dimensional Nature of Sports Equipment

• There are moments of inertia about equipment's three principal or dimensional axes
• Perimeter tape on tennis rackets increases shot speed and racket stability by increasing the polar moment of inertia against off-center effects
• Placing weight at the top of the frame would increase the moments of inertia for swinging the racket forward and upward, but not affect lateral stability
• Mass location variations on new baseball/softball bat designs allow for wide variation in the moment of inertia for a swing

Inertia Principal

• Can be expanded to biomechanical system angular motion
• The concepts related to moment of inertia are more difficult than mass in linear kinetics
• Putting on showshoes and a tennis player adding lead tape to the head of their racket quickly modify the racket's angular intertia

Decreasing Inertia

• Bring segment masses close to the rotation axis
• Coaches can get players to "compact" their extremities or body to make it easier to initiate rotation

Newton's Angular Analogues

• Rephrased using angular variables, Newton's Laws of Motion also apply to angular motion
• Newton's third law corollary is for every torque there is an equal and opposite torque
• The angular expression of Newton's second law. is the angular acceleration of an object is proportional to the resultant torque, is in the same direction, and is inversely proportional to the moment of inertia
• Newton's first law states those objects tend to stay in their state of angular motion unless acted upon by an unbalanced torque

Newton's Laws

• Used to calculate the net forces and torques acting on body segments by Biomechanists
• Working backward via video measurements of acceleration (second derivatives) using both the linear and angular versions of Newton's second law, is inverse dynamics
• Laborious hand calculations and graphing were used to create movement resultant forces and torques analyses

Calculations Today

• Aided by powerful computers Mathematical computation programs
• Resultant or net joint torques computed via inverse dynamics don't consider muscle group co-contraction
• Muscles, ligaments, joint contact, and other anatomical forces are represented

Inverse dynamics estimates

• Help to create human movement motor control signals
• Used to detect changes with fatigue or practice learning

Net Joint Torques

• Net joint torques at hip and knee in a soccer toe kick are illustrated in Figure 7.10
• Large hip flexor torque initiates the kick, decreasing rapidly
• The knee extensor torque mirrors the hip flexor torque

Kinetics

• It isn't easy to determine or understand the meaning of 3D kinetics, as large joint moment may have an negligibly little resistance arm & thus hardly promote wanted movement, or a movement that could well be required to position a portion to allow for one more torque in order to have the ability to speed up the portion.
• The product of a net joint torque and joint angular velocity can derive net joint powers
• Muscle action is primarily concentric if the product of a net joint torque and joint angular velocity are positive (moving in same direction) to produce positive work.

Negative Joint Powers

• Used to represent eccentric actions of muscle groups reducing the speed of a segment
• In order, analyze the net physical activity completed in respect to energy with time.
• Calculations are difficult since it modelling the transfer of mechanical energies in external body parts &segments

Equilibrium

• An important concept emerges from Newton's first and second laws
• Occurs when mechanical forces as well as movements that impacts the object sums up to reach zero

Newton’s second law

• Accounts for both straight line along , perpendicular state of being
• State being static which means the object either moves along the straight-line/ remains static continually

Dynamic Equilibrium

• Relates to moving systems as the second law states
• Force =ma T= I a In a way systems align themselves by having force go against each other. This is considered as the inertial resistance

Equilibrium text focus

• Examples are used showing force adding & removing for the object to be still. Still & the similar moving with a constant rate is equal

Equilibrium and Angular Kinetics

• Static equilibrium is used in determining how much center push is for human
• Used tools in having more object consistency

Joint angle affects muscle torque due to changes in moment arm and force-velocity. Torque-angle diagrams from isokinetic testing are U-shaped due to muscle moment arm and force-length relationship. Torque is beneficial for measuring muscular strength.