## Torque

The rotating effect of a force is called a torque or moment of force. Recall that a moment of force or torque is a vector quantity, and the usual two-dimensional convention is that counterclockwise rotations are positive. Torque is calculated as the product of force (F) and the moment arm. The moment arm or leverage is the perpendicular displacement (d±) from the line of action of the force and the axis of rotation (Figure 7.1). The biceps femoris pictured in Figure 7.1 has moment arms that create hip extension and knee flexion torques. An important point is that the moment arm is always the shortest displacement between the force line of action and axis of rotation. This text will use the term torque synony mously with moment of force, even though there is a more specific mechanics-of-mate-rials meaning for torque.

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Figure 7.1. The moment arms (dj for the biceps femoris muscle. A moment arm is the right-angle distance from the line of action of the force to the axis of rotation.

In algebraic terms, the formula for torque is T = F • d±, so that typical units of torque are N-m and lb •ft. Like angular kinematics, the usual convention is to call counterclockwise (ccw) torques positive and clockwise ones negative. Note that the size of the force and the moment arm are equally important in determining the size of the torque created. This has important implications for maximizing performance in many activities. A person wanting to create more torque can increase the applied force or increase their effective moment arm. Increasing the moment arm is often easier and faster than months of conditioning! Figure 7.2 illustrates two positions where a therapist can provide resistance with a hand dynamometer to manually test the isometric strength of the elbow extensors. By positioning their arm more distal (position 2), the therapist increases the moment arm and decreases the force they must create to balance the torque created by the patient and gravity (Tp).

Figure 7.2. Increasing the moment arm for the therapist's (position 2) manual resistance makes it easier to perform a manual muscle test that balances the extensor torque created by the patient (Tp).

Activity:Torque and Levers

Take a desk ruler (^12-inch) and balance it on a sturdy small cylinder like a highlighter. Place a dime at the 11-inch position and note the behavior of the ruler.Tap the 1-inch position on the ruler with your index finger and note the motion of the dime. Which torque was larger: the torque created by the dime or your finger? Why? Tap the ruler with the same effort on different positions on the ruler with the dime at 11 inches and note the motion of the dime. Modify the position (axis of rotation) of the highlighter to maximize the moment arm for the dime and note how much force your finger must exert to balance the lever in a horizontal position. How much motion in the dime can you create if you tap the ruler? In these activities you have built a simple machine called a lever.A lever is a nearly rigid object rotated about an axis. Levers can be built to magnify speed or force. Most human body segment levers magnify speed because the moment arm for the effort is less than the moment arm for the resistance being moved.A biceps brachii must make a large force to make a torque larger than the torque created by a dumbbell, but a small amount of shortening of the muscle creates greater rotation and speed at the hand. Early biomechani-cal research was interested in using anatomical leverage principles for a theory of high-speed movements, but this turned out to be a dead end because of the discovery of sequential coordination of these movements (Roberts, 1991).

Let's look at another example of applying forces in an optimal direction to maximize torque output. A biomechanics student takes a break from her studies to bring a niece to the playground. Let's calculate the torque the student creates on the merry-go-round by the force F1 illustrated in Figure 7.3. Thirty pounds of force times the moment arm of 4 feet is equal to 120 lb •ft of torque. This torque can be considered positive because it acts counterclockwise. If on the second spin the student pushes with the same magnitude of force (F2) in a different direction, the torque and angular motion created would be smaller because of the smaller moment arm (dB). Use the conversion factor in Appendix B to see how many N-m are equal to 120 lb •ft of torque.

Good examples of torque measurements in exercise science are the joint torques measured by isokinetic dynamometers. The typical maximum isometric torques of several muscle groups for males are listed in Table 7.1. These torques should give you a good idea of some "ballpark" maximal values for many major joints. Peak

Table 7.1

Typical Isometric Joint Torques Measured by Isokinetic Dynamometers

Peak torques

Table 7.1

Typical Isometric Joint Torques Measured by Isokinetic Dynamometers

Peak torques

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