# Mechanics mechanics that concerns the geometry of the

Mechanics is basically the study of forces and their effects on a body 2. A force tends to cause change of the state of a body at rest or when it is in uniform motion 1. Most forces involve magnitude and direction and can be shown as a vector with a specified point of application, shown by a line and an arrow that shows the direction of the force. An equilibrium is said to happen when all the forces acting on a body has a zero resultant force 1. In this case, the object would be in translational equilibrium when the vector sum of all the forces acting on the body is zero, where translational means only the positional changes are considered and the orientational change of the object with respect to the axes are not taken into account 4.
Biomechanics is then the applying of mechanical laws to the locomotor system of the human body and looks at the interrelations of the skeleton, muscles and joints, where the bones act as the levers, the ligaments binding the joints together form hinges, and the muscles provide the forces for moving the levers about the joints 2.
Kinematics is a part of mechanics that concerns the geometry of the motion of objects, which uses displacement, velocity, and acceleration, without considering the forces which produce the motion of the object 2. Kinetics, however, studies relationships between the force system acting on a body and the changes made by the body in motion.
Consider an object that has forces acting on it. All the forces acting on the object must be considered. In a biomechanics example, a person standing on both feet will have upwards force by the floor on each foot and downwards force on the person by gravitational pull, that is, a single downward gravitational force acting on the center of gravity of the person’s body 4 but this does not mean that a translational equilibrium needs to have forces acting at one point of the object only. Take a person’s leg at rest as an example, there would be three forces exerted on the leg, which are F1, the upwards force by the floor on the bottom of the foot, F2, the total forces from the rest of the body on the leg through the hip joint and surrounding muscles, and F3, the force acting along the line between F1 (acting on the bottom of the leg) and F2 (acting on the top of the leg). The leg would be in translational equilibrium when the sum of these forces is zero, where the points of application of the forces are ignored.
In biomechanics of joints, there are basic mechanical principles applied to some of the major joints such as the skeletal muscles, limbs as levers, the elbow, the hip, the back of the body, and the foot. The dynamic aspects of posture also plays a role in biomechanics of joints.
Skeletal movements are produced by skeletal muscles which consists of thousands of parallel fibers enveloped in an elastic sheath, narrowing at both ends into tendons 3. Tendons are made of strong tissue, which grows into the bone and functions to connect the muscle to the bone. Some muscles end in two or three tendons which are the biceps and triceps respectively. Before understanding how biceps and triceps as well as the limbs work, it is necessary to proceed with studying about levers.
A lever is defined as a stiff and inflexible rod freely rotating about a fixed point called the fulcrum, fixed so that it does not move with respect to the rod 3.  Levers make it easier to lift loads from one point to another. There are three classes of levers of which the focused class is the Class 3 lever. A Class 3 lever is the one with the fulcrum at one end, the load at the other, and between the two is where the force is applied. Limb movements of animals are performed by Class 3 levers. The force F needed for equilibrium with a load of weight W is given by
(Eq. 1)
where d1 and d2 are the lever arms lengths and d1 is the length from the fulcrum to the load and d2 is the length from the fulcrum to the force applied 3.
The mechanical advantage M of the lever is defined as
(Eq. 2)
A Class 3 lever has d1 greater than d2, hence, the mechanical advantage is always less than one.
The biceps and triceps are two most important muscles for the movement of the elbow, where the triceps produces an extension of the elbow by contracting, and the contraction of the biceps closes the elbow 3. An example would be a weight W held in a hand with its elbow bent at an angle. The weight causes the arm to have a downward pull and an upwards force is acting on the lower arm. The calculations done under the conditions of equilibrium, and considering the arm position as a Class 3 lever, will determine the pulling force Fm exerted by the biceps muscle and the direction and magnitude of the reaction force Fr at the joint, which is considered as the fulcrum. There are three unknown quantities to be calculated in this situation: the muscle force Fm, the reaction force at the fulcrum Fr, and the angle of direction of the force ?. The angle ? of the muscle force is found using trigonometric considerations. The sum of the x and y components of the forces need to be zero for each to have an equilibrium. So,
x components of the forces: (Eq. 3)
y components of the forces: (Eq. 4)
Another equation needs to be used in order to complete the findings of the unknown quantities, which is using torque for equilibrium, where the turning moments about any point is zero. It is easier to use the fulcrum as the point of torque, so the torque about the fulcrum is zero. The two torques involved would be clockwise due to the weight and counterclockwise due to the vertical component of the muscle force and the reaction force Fr acts at the fulcrum so its torque is zero about this point. The hip joint can also be represented as a simplified lever.
The hip is held in its socket by a group of muscles represented as a single resultant force Fm.  A person standing upright gives an angle to the force with respect to the horizon. The total weight of the leg, foot and thigh is represented by Wl, assuming it acts vertically downwards at the midpoint of the limb. In order to calculate the magnitude of the muscle force Fm and the force Fr at the hip joint when this situation happens, that is, the person is standing upright on a foot as the person would in a slow walk, the reaction force of the ground on the person’s foot is the force W acting on the bottom of the lever which supports the body’s weight. The above equations are used again to solve for the unknown quantities, using the x and y components as well as the torque about the fulcrum point. People with an injured hip walks in a limp as they lean towards the injured side while they step on that foot. This results in the shifting of the center of gravity of the body so it is directly above the hip joint. This results in the decrease of the magnitude of the force on the injured area. There is also an injury that can be caused by wrong positioning, which is the common back ache.
A back ache can happen when lifting a heavy object such as a trunk by bending the back. The spine pivots on the fifth lumbar vertebra when the trunk is bent forward from the vertical with the arms freely hanging 3. The pivot point now would be the fifth lumbar vertebra and the back is represented as the lever arm. The weight of the trunk is W1 and is uniformly distributed along the back and the effect of this force is illustrated as a weight suspended in the middle. W2 is the weight of the head and arms and is suspended at the end of the lever arm. Calculations for this scenario shows that it is not recommended to lift a weight with this position as it leads to backaches due to large forces acting on the fifth lumbar vertebra.
The foot is another major example of biomechanics. When a person tiptoes, the total weight is supported by the reaction force at a point and this is categorized as a Class 1 lever where the point of contact of the tibia is the fulcrum. For a Class 1 lever system, d1 is the distance between the load and the fulcrum and d2 is the distance between the fulcrum and the applied force, where the load is at the end of the lever arm, and at the other end of the lever arm is the applied force. The fulcrum is in between those two. The muscle which is joined to the heel by the Achilles tendon gives the balancing force. Calculations from 3 proves that standing on tiptoe is an exhausting position.
The act of standing upright needs the human body to be in a continuous swaying motion in order to maintain the center of gravity over the support base. An experiment was designed to analyse this aspect of stance, where the individual was told to stand, feet together, and as motionless as possible, on a platform that records the applied forces by the soles of the feet, known as the center of pressure. The compensation for the swaying movement of the center of gravity, this center of pressure is regularly shifting by a few centimeters over the soles area every half of a second. A constant minor deviation of the center of the mass with displacements about less than 1.5 cm are rectified by ankle movements 3. Hip movements  are needed to recompense grater displacements along with left and right sways. Balancing the body when walking requires more complex compensation movements. This is because of the change in center of gravity from one foot to the other.
A part of the body dynamics relates the musculoskeletal system. In one way or another, all muscles and bones are connected to each other. A shift in a muscle tension or limb position  is recompensed by a change in another part of the body. The right functioning of this kind of a arrangement requires the forces be distributed over all the bones and muscles. For example, excessive tightness from overexertion of the thickset muscles at the front of the legs will prone to have the torso pulled forward. In order to recompense this forward pull, the back muscles tighten as well which will usually applies force on the lower back and reflected as pain.  