2.  Torque is the cross product between a force and the distance of the force from a fulcrum (the central point about which the system turns). τ = r × F

3.  For a lever in mechanical equilibrium, sum of all the torques acting is zero or the total anticlockwise moment (torque) is equal to the total clockwise moment

4.  M. A. = Load = Effort arm Effort Load arm If the effort is farther from the fulcrum than the load (effort arm >load arm) then the lever is at mechanical advantage and is a force multiplier. If the effort is closer to the fulcrum than the load (load arm> effort arm) then the lever is at mechanical disadvantage and a speed multiplier.  The muscoskeletal system is designed for speed and range of motion rather than high force production

6.  The arrangement of muscles, bones and joints in the body form lever systems To figure out which type of lever is formed carefully look for  The point of muscle insertion where force is applied  Locate the joint about which movement is carried out. It is the fulcrum  Load or resistance is the part of the body to be lifted or moved. Its weight acts at its center of gravity  Note the force arm and load arm

8.  When we rise on tiptoe it is the muscles of the calf which raise the heel, the fulcrum is at the toes, and the weight of the body falls on the ankle after the fashion of a lever of the second order

9.  Most levers in the body are third order levers designed to maximize the speed rather than maximize the force

11.  Suppose a person is holding his/her forearm in a horizontal position with the upper arm vertical  The biceps muscle pulls the arm upwards by muscle contraction with a force F, the opposing force is the weight of the arm W at its center of gravity (CG)  The weight of the average person’s forearm (and hand) is about 2% of the total body weight. Say if a person weighs 72kg then the weight of his forearm is about 1.44kg Sum of clockwise torques= Sum of anticlockwise torques 14W=4F F=14W/4 For W= 15N, F= 52.5 N

12.  Let’ complicate the problem. Suppose now the person is holding a ball with weight of 44N

13.  The force in the biceps is quite large about twenty six times the weight of the arm and about ten times the weight of he ball  For mechanical equilibrium, the forces must balance. This means that 383N upward force must be balanced by the downward forces  Therefore a 324N downward force is exerted on the elbow due to weight of the bone in the upper arm

14.  Skeletal muscles typically work at a mechanical disadvantage so that they must exert a much greater force than the actual load to be moved  However lever arrangement enables muscles to move loads faster over greater distance than would otherwise be possible

15.  The force developed by biceps is independent of the angle between the lower and upper arm The lower arm can be hold by the biceps muscle at different angles  What muscle forces are required for the different arm positions?

16.  The curvature of deltoid muscle is important. If the force applied by the deltoid muscle passed directly through the fulcrum, there would be no torque  With the deltoid muscle angled slightly upward from the horizontal arm, the direction of the force does not go through the pivot point, giving a small nonzero lever arm

18.  If the point of insertion of deltoid muscle is 15cm from the shoulder joint  Weight of the arm is 5% of an average person’s weight. Say it is 36N and acting at the center of gravity of the arm at a distance of 25cm from the shoulder joint  The force in the deltoid muscle comes out to be 356N which is about ten times the weight of the arm. If an object weighing 10N is held at a distance of 64cm from the joint the force in deltoid muscle goes upto 590N  The reason here again is that effort arm is much smaller than the load arm

19. Latissimus dorsi muscle

20.  Gravitational force W applies at the center of gravity CG of the body. The center of mass of a body can be thought as a point about which the mass of the body is evenly distributed  CG depends on body mass distribution. Raising the arms over head lifts CG while bending at hips and knees lowers it. The higher the CG less stable a person is

21.  The key to stable equilibrium is that the center of gravity of the object must be over a large enough base.  A vertical line through the center of gravity must fall within its base of support.

22.  A person will be in stable equilibrium if he is standing with his center of gravity lying over the base formed by his feet. If he spreads his feet apart then he has a wider base and will be more stable. If he pulls his feet together he can be still stable but less so  This works even if the person stands on one foot but then he has to shift his body such that his center of gravity is over his feet. He can do this if he thrusts his hips in one direction and his shoulders in other direction, changing the shape of his body and location of his CG

26.  Applied Biomechanics: Concepts and Connections b y John McLester, Peter St. Pierre  Bios Instant Notes in Sport and Exercise Biomechanics b y Paul Grimshaw  Conditioning For Strength And Human Performance b y T. Jeff Chandler, Lee E. Brown