Mechanics in Exercise: Levers

Levers | First | Second | Third | Length | Variable


Movement in the body is produced by a system of levers. These series of levers work together to produce coordinated action, some by actual movement (dynamic) and others by stabilization (static).

  • Definitions
    • Lever: Rigid bar that turns about an axis of rotation or a fulcrum (A)
    • Motive Force (F): effort or exertion applied to cause movement against resistance or weight
    • Resistive Force (R): opposes motive force

First Class Lever

  • axis is placed between force and resistance
  • examples: crowbar, seesaw, scissors
  • examples in body:
    • elbow extension
      • triceps applying force to olecranon (F) in extending the non-supported forearm (R) at the elbow (A)
    • flexing muscle
      • agonist (F) and antagonist (R) muscle groups are simultaneously contracting on either side of a joint axis (A).

  • lever characteristics
    • balanced movement
      • axis is midway between force and resistance
      • e.g.: seesaw
    • speed and range of motion
      • axis is close to force
      • e.g.: elbow extension
    • force
      • axis is close to resistance

Second Class Lever

  • resistance is between axis and force
  • classic examples: wheelbarrow, nutcracker
  • complex example: rowing
    • paddle in water acts as slipping axis (A)
    • boat resistance is resistive force (R)
    • rower is motive force (F)
  • relatively few examples in body
    • plantar flexion of foot to raise body up on toes
      • ball of foot (A) serves fulcrum as ankle plantar flexors apply force to calcaneus (F) to lift resistance of body at tibial articulation (R) with foot.
    • entire body during push-up
      • foot is axis of rotation (A) when reaction force of ground pushing against hands (F) lifts weight of body's center of gravity (R).
  • lever characteristics
    • produces force: large resistance can be moved by a relatively small force
    • weight machines: more resistance needed, lower inertia, smoother feel.

Third Class Lever

  • force is placed between the axis and resistance
  • examples:
    • tongs: food (R) is supported by grip on handles (F) while axis is on opposite end.
    • shovelling: dirt on shovel (R) is lifted by force to handle by hand (F) while upper hand on end of shovel handle serves as axis (A)
    • rowing: oar is moved through water (R) by pulling on middle of oar (F) while holding end of oar with opposite hand (A).
      • Note: shovelling and rowing actions can also be first class lever systems if the hand closes to the force remains stationary (A) and the hand on the far end of the shovel or oar is moved (F).
    • batting: ball is hit (R) by moving bat toward ball with hand of far arm (F) while supporting lower portion of bat with hand of near arm (A).

  • example in body
    • most levers in body are third class
    • elbow flexion
      • Biceps and brachialis pull ulna (F) lifting the forearm, hand, and any load (R) at the elbow (A).
    • knee flexion
      • hamstring contract (F) to flex the lower leg (R) at the knee (A).
  • lever characteristics
    • produces speed and range of motion
    • requires relatively great force to move even small resistances
    • weight machines: less resistance required, greater inertia
      • harder to start and stop movement

Lever Arm Length

  • Definitions
    • Resistance Arm: distance between axis and point of resistance application.
    • Force Arm: distance between axis and point of force.
  • Formula
F x FA = R x RA
Force x Force Arm = Resistance x Resistance Arm
  • Example:
Initial Example Change insertion 1 cm Change point of resistance 1 cm
F x 2 cm = 10 kg x 9 cm
2 F = 90 kg
F = 45 kg
F x 3 cm = 10 kg x 9 cm
3 F = 90 kg
F = 30 kg
F x 2 cm = 10 kg x 8 cm
2 F = 80 kg
F = 40 kg

  • Lever characteristics
    • Long resistance arm: speed and range of movement
    • Short resistance arm: force
  • Mechanical advantage
    • Motive force arm length / Resistive force arm length
    • No mechanical advantage if quotient = 1 (same length):
    • If quotient >1: mechanical advantage in force
    • If quotient <1: mechanical advantage in speed and range of motion
  • Lever length of resistive forces
    • Center of gravity of body segment (eg: forearm in arm curl, body during push-up, etc.)
    • Center of gravity of any additional weight. (eg: handle on barbell, sand bag on back, etc.)
  • Perpendicular distance from fulcrum
    • When calculating forces applied to levers, the Perpendicular Distance from the fulcrum needs to be measured.
    • Torque = Force x Perpendicular Distance.
    • The physical distance and the perpendicular distance are the same only when force is being applied at a right angle (perpendicular) to the lever.
    • Perpendicular distance can be calculated by multiplying the physical distance x sine of the angle of force application. Also see Force Vectors and example below.

Variable Resistance Levers

  • Example
    • Universal gym equipment

Resistive force (R) is initially relatively short [close to fulcrum (A)].

Resistive force (R) is initially relatively short [close to fulcrum (A)].

As motive force (F) acts on lever, resistive arm becomes physically longer, yet its perpendicular distance remains constant. In contrast, motive torque diminishes, requiring progressively greater motive force throughout movement.

Even though the physical distance between (R) resistive force and (A) fulcrum increases approximately 2 fold, perpendicular distance is the same. You can more clearly see this by drawing a line in the direction of (R) resistive force and a parallel line through (A) fulcrum. Since gravity acts on the weight in our diagram, the (R) resistive force is downward, so both lines will be drawn vertically. The distance between the lines (perpendicular distance) are the same in each diagram, therefore the resistive torque remains constant.

In contrast, although the physical distance between (F) motive force and (A) fulcrum do not change, their perpendicular distance decrease. To see this, draw a line in the direction of the (F) motive force and a parallel line through the (A) fulcrum. But in this case, the distance between the lines (perpendicular distance) decrease, therefore the motive torque diminishes as it moved downward, requiring greater (F) motive forces to raise the (R) resistive forces.

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