Basic trigonometry for biomechanics

In summary, "Hulk" Heise is doing leg curls on a Cybex machine and gets stuck with a 90° angle at the knee joint. The force exerted by the machine (FA) is 500 N at an angle of 55° relative to the tibia, with a distance of 55 cm from the knee joint to the point of application. The length of the moment arm from the knee joint to the applied force (FA) can be found using trigonometry. The torque created by the applied force (FA) about the knee joint can also be calculated. To balance or offset the extension torque created by FA, the hamstrings (FM) must exert a force. This exercise is applied to a
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Bodybuilder “Hulk” Heise is doing leg curls on a Cybex machine. “Hulk” gets stuck (see figure) with 90° angle at the knee joint. The force exerted by the machines (FA) on his leg is 500 N, directed at an angle of 55° (angle α) relative to the tibia, and the distance from “Hulk’s” knee joint to the point where the force is being applied is 55 cm (distance L). For this problem, assume the weight of the shank and foot is negligible and the muscle force (FM) acts perpendicular to the tibia in this position.

a. What is the length of the moment arm from the knee joint to the applied force (FA)? (hint: drawing a line and use trigonometry will help)
__________
b. What is the torque created by the applied force (FA), about the knee joint? __________
c. After finding the torque above, how much force is required from the hamstrings (FM) to balance or offset the extension torque created by the applied force (FA) (note: moment arm for the line of action of hamstring is given)
__________
d. Which lever is this exercise applied to (circle one)
1st lever 2nd lever 3rd lever
 

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FAQ: Basic trigonometry for biomechanics

1. What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems involving angles and distances, and is essential in many fields including biomechanics.

2. How is trigonometry used in biomechanics?

Trigonometry is used in biomechanics to calculate the forces and movements of the human body. By using trigonometric functions such as sine, cosine, and tangent, biomechanists can analyze the angles and forces involved in various movements and activities.

3. What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent. Sine (sin) is the ratio of the opposite side to the hypotenuse, cosine (cos) is the ratio of the adjacent side to the hypotenuse, and tangent (tan) is the ratio of the opposite side to the adjacent side.

4. How can I apply trigonometry to calculate joint angles?

To calculate joint angles using trigonometry, you will need to measure the lengths of the sides of the triangle formed by the bones at the joint. Then, you can use the inverse trigonometric functions (arcsine, arccosine, arctangent) to find the angles of the triangle and determine the joint angle.

5. What are some common trigonometric formulas used in biomechanics?

Some common trigonometric formulas used in biomechanics include the law of cosines (used to find the length of a side of a triangle), the law of sines (used to find the measure of an angle in a triangle), and the Pythagorean theorem (used to find the length of the hypotenuse in a right triangle).

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