LEVERS Some “rigid” structure that is hinged at one point and has two forces applied at other points. 5/21/2019 Dr. Sasho MacKenzie - HK 376

Lever Terms The hinge or pivot point is known as the fulcrum ( ). One of the forces is the resistance force (FR) and opposes the intended movement. The other force is the applied force (FA) and that causes or tends to cause the lever to move. 5/21/2019 Dr. Sasho MacKenzie - HK 376

Lever Arms (Moment Arms) There are two lever arms for every lever. One associated with each force. The resistance lever arm (dR) is the perpendicular distance from the line of action of the resistance force to the fulcrum. The applied lever arm (dA) is the perpendicular distance from the line of action of the applied force to the fulcrum. FA FR dA dR 5/21/2019 Dr. Sasho MacKenzie - HK 376

Levers: What are they for? Oars, vaulting poles, golf clubs, and wheels are all levers, but the most important levers in kinesiology are bones and the muscles that move them. Levers can do two things Increase Force Increase Speed 5/21/2019 Dr. Sasho MacKenzie - HK 376

Levers can Increase Force A lever can increase the effect produced by a muscular force. In other words, a smaller muscular force may balance out a greater resistance force. FA FR dR dA Weight of head 50 N Trapezius dA = 5 cm dR = 2 cm The force of the trapezius to hold the skull in equilibrium is given by: FA x 5 cm = 50 N x 2 cm FA = 20 N 5/21/2019 Dr. Sasho MacKenzie - HK 376

Levers can Increase Speed A lever can increase the speed of an object. A relatively slow hand speed can result in a very high clubhead speed In this golf example, the right hand is the applied force and moves 10 cm in the last phase of the swing, while the clubhead travels 100 cm. The left wrist is the fulcrum. FR FA 10 cm 100 cm Both of these distances are covered in the same period of time. Hence the clubhead speed is 10 times that of the right hand. 5/21/2019 Dr. Sasho MacKenzie - HK 376

Mechanical Advantage M.A. = dA dR Mechanical advantage or leverage is the ratio of how much force you get out relative to how much you put in. The ratio of the applied force lever arm (dA) to the resistance force lever arm (dR). M.A. = dA dR FR FA dR = 1 dA = 2 M.A. = dA = 2 = 2 dR 1 5/21/2019 Dr. Sasho MacKenzie - HK 376

First Class Levers The fulcrum lies between the points of applied force and resistance force. Examples: See-Saw, scissors, pliers FR FA dR dA First class levers can be used to gain a mechanical advantage by increasing the length of the applied lever arm (dA). First class levers can also be used to increase the speed of movement by decreasing the length of the applied lever arm (dA). 5/21/2019 Dr. Sasho MacKenzie - HK 376

Second Class Levers The fulcrum lies at one end, and the applied lever arm is greater than the resistance lever arm. Examples: Bottle opener, wheel barrow, nut cracker dR FR FA dA Second class levers can only be used to increase the effect of an applied force. 5/21/2019 Dr. Sasho MacKenzie - HK 376

Third Class Levers The fulcrum lies at one end, and the resistance lever is greater than the applied lever arm . Examples: Tweezers and Tongs dA FR FA dR Third class levers can only be used to increase the speed of movement of the load. 5/21/2019 Dr. Sasho MacKenzie - HK 376

Lever Arm is Moment Arm FA A A FR = mg The brachioradialis is a 3rd class lever because the resistance lever arm is greater than the applied lever arm. dA dR 5/21/2019 Dr. Sasho MacKenzie - HK 376

Calf Raise Example B A C Vertical Joint Reaction Force ? Vertical Component of Achilles Tendon Force? B A *Assume Static Equilibrium Determine unknown forces. What class of lever? Does it increase speed or force? What is the M.A.? 0.05 m C 0.15 m 1000 N 5/21/2019 Dr. Sasho MacKenzie - HK 376

5/21/2019 Dr. Sasho MacKenzie - HK 376

Levers can Increase Speed A lever can increase the effective speed of a muscular contraction. A muscle contracting at 1m/s may displace the distal end of a bone at a rate of 10 m/s. In this kicking example, the quadriceps shorten by 10 cm, while the point of the foot in contact with the ball travels 100 cm. L = 100 cm L = 10 cm Both of these distances are covered in the same period of time. Hence the foot speed is 10 times that of the muscle contraction. FA FR 5/21/2019 Dr. Sasho MacKenzie - HK 376