Physics 160 Biomechanics

Torque

Questions to Think About

• What factors affect a muscle’s functional strength (i.e. ability to control rotation) at a joint?

• Why should a worker keep an object being lifted close to his torso in the transverse plane?

• What allows us to walk across the room?

Torque Torque is the measure of the extent to which a force will

cause an object to rotate. It is the product of the force and the force’s moment arm.

[ ][ ]

[ ]

T F dT torque in N mF force in Nd moment arm in m

⊥

⊥

= ⋅= ⋅==

Torque is a vector quantity that lies along the axis of rotation.

Line of Action of a Force

• The line of action of a force is the imaginary line that extends from the force vector in both directions.

• It’s the line that the force pushes or pulls along.

F Line of action of F

Moment Arm • Shortest distance from a force’s line of action to the

axis of rotation • Moment arm is always perpendicular to the line of

action and passes through the axis of rotation

Computing the Moment Arm • Determined by:

– Distance d from axis of rotation to point at which force is applied

– Angle at which force is applied

θ

d

d┴=d sinθ F

Axis of rotation

Line of Action The line of action of the three

forearm muscles. The brachialis (BRA) is a large muscle, but it has the smallest moment arm, giving it the poorest mechanical advantage. The biceps brachii (BIC) also has a large cross-section and has a longer moment arm, but the brachioradialis (BRD), with its smaller cross-section, has the longest moment arm, giving it the best mechanical advantage in this position.

Example If the force due to the

biceps shown is 100N and the moment arm is 1.5 cm. What is the torque produced by the biceps?

Torque due to Muscles A muscle with a small moment arm (A) needs to

produce more force to generate the same torque as a muscle with a larger moment arm (B).

Moment Arms The magnitude of the moment arm of the biceps

muscle changes throughout the range of motion.

Positive and Negative Torque • Positive torque tends to cause counterclockwise

rotation • Negative torque tends to cause clockwise rotation

Example Find the torque produced by each child if the angle

of the teeter totter with the horizontal is 25o.

Example

Using the anthropometric data given in Appendix D determine if the two forces shown below create torques equal in magnitude?

Resultant Joint Torque • The effects of all forces acting across a joint can be

duplicated exactly by the combination of: – A resultant joint force acting at the joint center – A resultant joint torque acting about the axis of

rotation through the joint center. • Resultant joint force = the vector sum of all forces

acting across a joint. • Resultant joint torque = the sum of the torques about

the joint axis due to these forces. • Note: Forces that do not act across the joint are not

included (e.g. weight)

Shoulder girdle muscle forces

Segmental Representation of the Body

Segment com’s are marked with an “X”, total body com is the black dot

Torques during a Squat Joint forces are Fx and FY, W is the weight of each

segment and M denotes the torques acting at the joints.

Levers • A lever is a simple machine

consisting of a relatively rigid barlike body that can be made to rotate about an axis or fulcrum

• There are first, second and third class levers depending on the relative positions of F, the applied force, R, the resistance and the fulcrum.

F R

First class

R F

Second class

F R

Third class

Mechanical Advantage • The mechanical

advantage of a lever is the ratio of the moment arm of the force to the moment arm of the resistance.

• An anatomical lever showing the resistance arm, effort arm, and fulcrum (elbow joint).

First Class Levers • Effort force and resistance force on opposite sides of

the fulcrum • A first-class lever in which the mechanical advantage

is less than 1, that is, the effort arm is less than the resistance arm. The linear distance moved by the effort force, however, is less than that moved by the resistance force in the same time.

First Class Levers An anatomical first-

class lever in which the weight of the head is the resistance force, the splenius muscles provide the effort force, and the fulcrum is the atlanto-occipital joint.

Second Class Levers

The effort force and the resistance force act on the same side of the fulcrum. The resistance force is between the fulcrum and the effort force.

Mechanical advantage is greater than 1.

Third Class Levers The effort force and the

resistance force act on the same side of the fulcrum. The effort force is between the fulcrum and the resistance force.

The arm held in flexion at the elbow is an anatomical third-class lever: The resistance force is the weight of the arm, the fulcrum is the elbow joint, and the effort force is provided by the elbow flexor muscles.

Levers • 1st Class: Mechanical Advantage (MA) varies • 2nd Class: Favors the effort force

– MA > 1 (i.e., a smaller effort force can balance a larger resistive force)

• 3rd Class: Favors range and speed of movement. – MA < 1

• The majority of musculoskeletal systems are in third-class levers.