Levers and Torque

What is a lever?

A simple machine used to increase or decrease mechanical advantage.

What are the 3 components of a lever?

Load (L), Fulcrum (F/axis of rotation), and Effort (E/internal or external force).

What is the formula for mechanical advantage?

Mechanical advantage = Effort Arm (EA) ÷ Resistance Arm (RA).

What does a mechanical advantage greater than 1 mean?

The lever provides a force advantage.

What does a mechanical advantage less than 1 mean?

The lever provides a speed or distance advantage.

Describe a first-class lever.

Axis is between the effort and load; can be used for force or speed advantage; uncommon in the body.

Example of a first-class lever in the body.

Splenius muscles acting on the atlanto-occipital joint.

Describe a second-class lever.

Load is between the axis and the effort; provides a force advantage; uncommon in the body.

Example of a second-class lever in the body.

Raising the heels off the ground (plantarflexion).

Describe a third-class lever.

Effort is between the axis and the load; provides a speed/distance advantage; most common in the human body.

Example of a third-class lever in the body.

Biceps curl.

Define torque.

A turning or rotational force; product of force × perpendicular distance from the axis of rotation (moment arm).

Torque formula.

T = F × d (Force × perpendicular distance).

Define moment arm.

The perpendicular distance from the axis of rotation to the line of action of the force.

What is the branch of mechanics that deals with forces when no motion occurs?

Statics.

Conditions for static equilibrium.

ΣF = 0 and ΣM = 0 (sum of forces and moments equals zero).

Equation for sum of the moments in equilibrium.

ΣMcw = ΣMccw (clockwise moments equal counterclockwise moments).

What happens when ΣM ≠ 0?

The object rotates or accelerates.

If an object is not moving, what must be true about the sum of moments?

They must equal zero.

How to solve for an unknown force using moments.

Set Force A × Moment Arm A = Force B × Moment Arm B, then solve for the unknown.

Example problem: If Force A = 10 N at 2 m, Moment Arm B = 4 m, what is Force B?

Force B = 5 N (10×2 = 4×B → B = 20/4).

Define static rotary equilibrium.

When internal and external torques are equal, resulting in no angular movement.

What is internal torque?

Torque produced by muscle contraction.

What is external torque?

Torque produced by gravity or external forces.

In the elbow, which direction does the external torque act?

Clockwise (downward pull of gravity).

In the elbow, which direction does the internal torque act?

Counterclockwise (muscle contraction).

What happens when internal torque > external torque?

The segment moves in the direction of the internal torque (e.g., flexion).

What happens when external torque > internal torque?

The segment moves in the direction of the external torque (e.g., extension under gravity).

How does joint position affect moment arm length?

Joint angle changes the perpendicular distance, altering torque potential.

Where does gravity have the greatest moment arm on the lower leg?

When the segment is horizontal.

Where does the biceps muscle have the greatest moment arm?

At midrange of elbow flexion.

Order of primary elbow flexors by longest moment arm.

Brachioradialis > Biceps brachii > Brachialis > Pronator teres.

How does moment arm length change through ROM?

It varies; muscles peak in torque at midrange due to optimal moment arm and length-tension.

Muscles with larger moment arms must do what to achieve same ROM?

Shorten more than muscles with smaller moment arms.

How does a greater moment arm affect torque production?

A greater moment arm allows more torque if the same force is applied.

What is vector resolution?

Breaking a muscle’s total force into its perpendicular (rotary) and parallel (stabilizing) components.

What component of muscle force causes rotation?

The perpendicular component (Fy).

What component of muscle force causes compression or distraction?

The parallel component (Fx).

Formula to find perpendicular component (Fy).

Fy = F × sin(θ).

Formula to find parallel component (Fx).

Fx = F × cos(θ).

If a muscle produces 50 N at a 30° angle, what are the components?

Fy = 25 N (rotation), Fx = 43.3 N (compression).

What type of force does a perpendicular line of pull cause?

Rotary force.

What type of force does a parallel line of pull cause?

Translatory (compression or distraction) force.

What is a free body diagram (FBD)?

A visual model that shows all forces acting on an isolated segment.

Purpose of a free body diagram.

To analyze internal and external forces, torques, and motion on a segment.

In an FBD of the forearm, what does L represent?

Gravitational force acting on the limb.

In an FBD of the forearm, what does W represent?

External weight held in hand.

In an FBD of the forearm, what does M represent?

Muscle force vector.

In an FBD of the forearm, what does E represent?

Axis of the elbow joint.

What happens if a therapist applies force further from the axis of rotation?

Torque increases (greater mechanical advantage).

How can therapists manipulate torque during manual resistance?

By adjusting hand placement relative to the joint axis.

If torque is greater at distal tibia vs mid-tibia, what does this mean?

The farther the force from the axis, the greater the torque required to resist it.

What is the relationship between torque and distance?

Torque increases as the perpendicular distance from the axis increases.

What is the unit for torque?

Newton-meters (N·m) or Newton-centimeters (N·cm).

What is the practical PT application of torque and lever systems?

Helps assess joint strength, muscle function, and mechanical efficiency.