Biomechanics Concepts: Mechanical Advantage Worked Problem

Jacob Goodin

18d • Discussion/Announcements

Worked mechanical advantage problem

Scenario: A lifter is holding a 20 kg dumbbell during a biceps curl at a fixed elbow angle.

At this position:

The distance from the elbow joint to the dumbbell’s line of force (external moment arm) is 0.30 m
The biceps’ internal moment arm is 0.04 m
Gravity is 9.8 m/s²

Mechanical advantage = internal (muscle) moment arm ÷ external (load) moment arm

Step 1 — Determine the external force

The weight of the dumbbell (in Newtons) is found by multiplying mass by gravity.

20 kg × 9.8 m/s² = 196 N

So the external force acting on the elbow is 196 newtons.

Step 2 — Calculate external torque at the elbow

External torque equals the external force multiplied by the external moment arm.

196 N × 0.30 m = 58.8 N·m

So the elbow must resist 58.8 newton-meters of torque.

Step 3 — Determine required biceps force

To hold the position without movement, the torque produced by the biceps must equal the external torque.

58.8 N·m ÷ 0.04 m = 1470 N

So the biceps must produce approximately 1470 newtons of force to hold the dumbbell at that joint angle.

Step 4 — Mechanical advantage

Mechanical advantage is the ratio of the muscle’s moment arm to the external moment arm.

0.04 m ÷ 0.30 m = 0.13

This means the biceps muscle has a low mechanical advantage at this position.

Coach takeaway:

Even though the dumbbell only weighs 20 kg, the biceps must produce a much larger force because the external moment arm is long and the muscle moment arm is short.

1 comment