Biomechanics

Biomechanics studies the movements and forces acting on living organisms, applying the principles of physics and mechanics. It finds its applications in health and sports: understanding injuries, athletic performance, design of medical devices.

Discover FizziQ

How to measure it in class

The FizziQ app turns the smartphone into a body-worn sensor: accelerometer, gyroscope and video analysis make it possible to quantify a human movement without laboratory equipment.

Steps:

• Attach the smartphone as close as possible to the center of mass (belt, lower back): this is the position that gives the signal most representative of the overall movement of the body.
• Select linear acceleration (without g) and start recording, then perform the movement being studied: walking, running, squat, vertical jump.
• Identify on the curve the phases of the movement: run-up, support, flight, landing. Each phase translates into a characteristic acceleration pattern.
• For a vertical jump, measure the flight duration between takeoff and landing, when the linear acceleration is close to zero, and deduce the height.
• Film the same movement from the side, then use FizziQ’s video analysis module to track a joint frame by frame and obtain its trajectory.
• Compare the recordings of several students: the spread between individuals is much greater than the spread between two attempts by the same student.

Scientific activities on this topic

Smartphones are extremely useful tools as measuring instruments for biomechanics. Scientists can use the various sensors to gather detailed information about the position, rotation and speed of the body, but they can also record detailed videos or chronophotographs of movements with the camera, which can be analyzed with software like FizziQ.

Below you will find a number of experiments on physics and sport to carry out with FizziQ:

• Parabolic trajectory of a basketball
• Speed of a skier during the Olympic games
• Center of gravity of a diver
• Determining the phases of the pole vault
• Measure your heart rate with the accelerometer (accelerocardiogram)
• Photoplethysmography of a finger: detect the pulse with the camera
• Pedometer and step detection in the acceleration signal

Learn more

A history that begins in the Renaissance

The beginnings of biomechanics date back to the Italian Renaissance, when Leonardo da Vinci (1452-1519) studied human anatomy and body movements, notably in his famous Vitruvian Man study. But the true birth certificate of the discipline is the treatise De Motu Animalium, published in 1680 by Giovanni Alfonso Borelli, a student of Galileo: in it he applies for the first time statics and the theory of levers to muscles and joints, and computes the muscular forces required for walking, running and the flight of birds. In the 19th century, the German surgeon Julius Wolff (1836-1902) states in 1892 “Wolff’s law”: living bone remodels itself according to the mechanical stresses it undergoes. It is one of the founding principles of tissue biomechanics, still studied today.

Measuring movement

At the end of the 19th century, the French physiologist Étienne-Jules Marey and the British photographer Eadweard Muybridge invent chronophotography and make human and animal movement measurable frame by frame. Marey also builds the first force platforms. In the 1950s and 1960s, high-speed cameras, force platforms and electromyography make biomechanics a fully experimental discipline. A smartphone equipped with an accelerometer and a camera today carries these two historical instruments in a pocket.

The body is not a rigid solid

This is the point that distinguishes biomechanics from point mechanics. A human body is modeled as a kinematic chain: about fifteen segments considered rigid (foot, lower leg, thigh, trunk, upper arm, forearm, hand, head), connected by joints that each allow one or more degrees of freedom. The body’s center of mass is therefore not a fixed point of the body: it moves when posture changes, and it can even lie outside the body, for example outside the back of a high jumper clearing the bar in an arched position. This is what allows the center of mass to pass under the bar while the body passes over it.

Internal forces far exceed the weight

A frequent misconception is to believe that a muscle exerts a force of the same order as the load being lifted. This is false, because of lever arms. In the forearm, the biceps inserts about 4 cm from the axis of the elbow, whereas the load held in the hand is about 32 cm away. The balance of moments therefore requires from the biceps a force about 8 times greater than the load: holding 5 kg in the hand demands from the biceps a force of the order of 400 N, the equivalent of 40 kg. The body is almost everywhere a system of unfavorable levers, which favors the amplitude and speed of the movement at the expense of force. This is also why the stresses on joints and tendons are much greater than the weight lifted, and why injuries occur there.

The biomechanics of sport

Biomechanics is used to improve sports performance, in particular by helping athletes train more effectively, improve their performance and avoid injuries. For example:

1. Running: Biomechanics is used to analyze runners’ movements and identify factors that can affect their performance. Biomechanics researchers can study the position of runners’ feet and legs during running to determine the best running technique and minimize the risk of injury.

2. Swimming: Biomechanics is used to improve swimmers’ technique by analyzing their position, movement and force in the water. Researchers can study glide angles, propulsion efficiency and the trajectory of arm and leg movements to help swimmers improve their performance.

3. Jumping: Jumps such as the high jump, pole vault and long jump require precise technique to maximize the height or distance of the jump. Biomechanics researchers can study body movements during the jump to optimize jumping technique and minimize the risk of injury.

4. Throwing: Throwing events, such as shot put and javelin, depend on throwing technique to maximize the distance of the throw. Biomechanics can be used to analyze the position, force and trajectory of the throw to improve technique and maximize distance.

Orders of magnitude

Biceps force to hold 5 kg with the arm bent: about 400 N. Ground reaction force when walking: about 1.1 to 1.2 times the body weight. When running: 2 to 3 times the body weight. On landing from a jump: 4 to 6 times the body weight, or even more on stiff heels. Mechanical power developed during a vertical jump: 1000 to 3000 W for a few tenths of a second. Height of a vertical jump without run-up: 0.3 to 0.4 m for a student, up to 0.8 m for an athlete. Walking cadence: 100 to 120 steps per minute.

Formula

The equilibrium of an articulated segment is written as an equality of moments about the axis of the joint:

F_muscle × d_muscle = F_load × d_load

where:

• F_muscle: force developed by the muscle (N)
• d_muscle: distance from the muscle insertion to the axis of the joint, the lever arm (m)
• F_load: force exerted by the load, here its weight (N)
• d_load: distance from the load to the axis of the joint (m)

The height of a vertical jump is deduced from the flight duration, measured between takeoff and landing:

h = g × t_flight² / 8

where:

• h: height of elevation of the center of mass (m)
• g: acceleration due to gravity, 9.81 m/s²
• t_flight: total flight duration (s)

The average mechanical power developed during the push-off phase is:

P = m × g × h / Δt

where:

• P: average mechanical power (W)
• m: mass of the jumper (kg)
• Δt: duration of the push-off phase (s)

Application examples

• A biceps inserts 4 cm from the elbow and supports a 5 kg load placed at 32 cm: the muscular force is 50 × 32 / 4 = 400 N, that is 8 times the weight of the load

• A vertical jump whose measured flight time is 0.50 s corresponds to an elevation of the center of mass of 9.81 × 0.25 / 8 ≈ 0.31 m

• A 70 kg runner undergoes at each footfall a ground reaction force of about 2000 N, that is nearly three times their weight

• Video analysis of a javelin throw makes it possible to measure the release angle and speed, the two parameters that set the range

• Designing a hip prosthesis requires knowing the actual stresses undergone by the joint, which reach 3 to 4 times the body weight when walking

• Studying the running of a patient in rehabilitation makes it possible to detect an asymmetry between the two footfalls before it causes an injury

FAQ

Q: Why should the smartphone be placed near the lower back? A: Because the body’s center of mass is located approximately at the level of the lumbar vertebrae, a little above the pelvis. A sensor placed there measures the overall movement of the body. Placed on the wrist or in a jacket pocket, it mainly records the swing of the limb, not the displacement of the body.

Q: Why must the biceps exert a force far greater than the weight lifted? A: Because its lever arm is very short, about 4 cm, while the load is more than 30 cm from the joint. The balance of moments then requires a muscular force about eight times greater. In return, a small contraction of the muscle produces a large, fast displacement of the hand.

Q: Can the human body be treated as a rigid solid? A: No, except over very short durations or for a movement where the body remains fixed. The body is a chain of articulated segments, and it is precisely the relative mobility of these segments that produces movement. Each segment, however, can be modeled separately as a rigid solid.

Q: Why can the center of mass lie outside the body? A: The center of mass is an average point weighted by the distribution of masses, it does not necessarily belong to the matter. When the body arches strongly, like a high jumper above the bar, this average point lies in the void, under the jumper’s back.

Q: Why do injuries occur mostly on landing from a jump? A: Because the deceleration there is very brutal. The momentum acquired during the fall must be canceled in a few hundredths of a second, which produces forces of several times the body weight. Bending the knees lengthens the duration of the impact and reduces the force undergone accordingly.

Related concepts

Center of Gravity - Accelerometer - Kinetic Energy - Human Physiology - Pedometer - Chronophotography