The study of the biomechanics of muscles and bones reveals how our bodies operate like complex simple machines. The forces within the body can be surprisingly large, often much greater than the external loads we handle. This is due to the geometry of skeletal muscles and how they attach to the bones via tendons close to joints. While this arrangement allows for quick and precise movement, it also means that the mechanical advantage of these systems is less than 1, requiring high internal forces from muscles.

Consider the human arm as illustrated in Figure 65.1. The biceps apply an upward force [latex]{F}_{\text{B}}[/latex] to hold a book stationary in the hand. This force must balance not only the downward force from the weight of the book but also the weight of the arm itself. Since the biceps tendon is attached very close to the elbow joint, the lever arm for [latex]{F}_{\text{B}}[/latex] is much shorter than that for the book’s weight, leading to a low mechanical advantage.

Let’s analyze the torques in this system to understand how much force the biceps must apply. Assume the arm is horizontal and stationary, meaning the net torque about the elbow (pivot) is zero:

Here:

• [latex]r_1[/latex] is the distance from the elbow to the point of biceps attachment,
• [latex]r_2[/latex] is the distance to the center of gravity of the arm,
• [latex]r_3[/latex] is the distance to the center of gravity of the book,
• [latex]w_{\text{arm}}[/latex] is the weight of the arm, and
• [latex]w_{\text{book}}[/latex] is the weight of the book.

Solving this equation gives us the required force from the biceps to keep the system in static equilibrium. Because [latex]r_1[/latex] is small, [latex]F_B[/latex] must be large to balance the torques created by the larger weights at longer lever arms. This explains why muscles generate forces far exceeding the loads they hold.

This arrangement, while inefficient in terms of force, is highly effective for fast and precise control of limb movement. Attaching muscles near joints minimizes the angular moment of inertia, making limbs easier to rotate rapidly—an evolutionary advantage for reflexive or coordinated motion.

Posture and Back Strain

Improper posture can create large torques in the back due to increased horizontal distances between the center of gravity and the spinal pivot. For example, when bending over with a load, the torque due to the load and the upper body weight increases dramatically if the load is held far from the spine. The back muscles must then exert very large forces to maintain equilibrium, which can lead to fatigue or injury.

To reduce back strain, it is essential to keep the load close to the body, reduce the total load, and bend the knees rather than the back, which allows the legs to support more of the weight.

The force a muscle can exert depends on its length and the angle of the limb. In the case of the biceps, as the forearm angle changes from 90°, the muscle shortens, reducing its capacity to generate force. This biomechanical limitation is due to the length–tension relationship in muscle fibers—muscles produce the most force when slightly stretched beyond their resting length.

Joint forces can also be surprisingly large. In the earlier example, the elbow joint experiences a downward force [latex]{F}_{\text{E}}[/latex] of about 407 N, which is over six times greater than the weight supported. This happens because the upward force by the muscle must counter not only the load’s torque but also its own geometry-induced mechanical disadvantage. For equilibrium:

These force magnitudes explain why injuries can occur even during seemingly light tasks, especially when the load is located far from the joint. Increasing the lever arm increases the torque required to maintain static equilibrium, thus increasing muscle force and joint stress.

Activities such as swinging a racquet or bat, particularly with poor technique or ill-fitted equipment, can cause excessive and repetitive torque on muscles and tendons. The phenomenon of “tennis elbow,” for instance, arises from repeated extension and torque applied to the elbow joint with low mechanical advantage. Proper grip, alignment, and targeting the racquet’s “sweet spot” can minimize the force transmitted through the arm and reduce injury risk.

Posture and Torque on the Spine

Figure 65.2 illustrates how posture affects torque on the hips and lower back. In part (a), good posture positions the upper body’s center of gravity (cg) directly above the pivot point at the hips, requiring only a vertical support force with minimal or no muscular effort. In this case, the torque about the pivot is zero:

However, in part (b), poor posture shifts the cg forward, creating a clockwise torque about the hips. This must be countered by large forces from the lower back muscles, which have a short perpendicular lever arm [latex]{r}_{\text{b} \perp}[/latex] relative to the cg’s moment arm. The required muscle force [latex]{F}_{\text{b}}[/latex] is therefore quite large:

Solving for the back muscle force gives:

Because [latex]r_{\text{cg}} \gg r_{\text{b} \perp}[/latex], the muscle force is much larger than the body’s weight. Prolonged muscle activity in this posture can lead to fatigue and back pain.

The rule of equilibrium requires that the overall center of gravity remain over the base of support (feet). When carrying loads, people instinctively adjust their posture to restore balance. This is shown in Figure 65.3, where a person leans forward with a child on their shoulders, leans sideways with a bag on one side, or leans backward when carrying books in the arms.

Takeaway on Lifting and Load Positioning

The torque on the spine and joints increases dramatically with poor load handling. Bending at the waist to lift something puts the load far from the back pivot point, increasing [latex]r[/latex] in the torque equation:

To reduce torque and associated muscle strain, always lift with your legs (reducing [latex]r[/latex]) and keep the object close to your body’s center of gravity.

Lifting with the back, as shown in Figure 65.4, requires extremely large muscle forces because the perpendicular distance between the pivot point (hip joint) and the muscle force vector is very short. Meanwhile, the horizontal distance to the load (e.g., a box) is much longer, which results in a large torque that must be counteracted. This is why lifting with the back rather than the legs increases the risk of injury due to disc compression or muscle strain.

Advantages of Close Muscle Attachment

Why are skeletal muscles typically attached close to joints, even though this results in small mechanical advantages? The primary advantage is speed. Small contractions of muscles near the joints produce larger angular displacements at the limb ends, which enables fast motion. This arrangement also supports greater flexibility and agility, allowing vertebrates to perform a wide variety of coordinated actions.

For instance, if the biceps muscle were attached far from the elbow—say, at the wrist—it would lose both the mechanical control and fine-tuned movement range that vertebrates rely on. The trade-off for low mechanical advantage is thus improved control, speed, and maneuverability.

Complexities in Real Biological Systems

In practice, many joints behave more like dynamic systems than simple levers. As a joint flexes or extends, the pivot point often shifts, which causes both the perpendicular lever arms and the mechanical advantage to change continuously. This makes the required muscle force variable throughout the motion.

For example, the force the biceps must apply to support a weight changes as the angle of the forearm changes, because the torque equation:

depends on both the angle [latex]\theta[/latex] and the effective distance [latex]r[/latex] from the pivot point. This is also why seat height on a bicycle affects leg strain—if the leg angle isn’t optimal, muscle force and torque increase unnecessarily.

Despite these complexities, the basic statics principles described here provide a useful approximation for analyzing biological systems. When enough information is available about bone lengths, muscle positions, and joint mechanics, accurate predictions of forces and torques can be made. A deeper biomechanical model would also include muscle elasticity, tendon stiffness, and dynamic loading.

Many real-world injuries, like joint damage and muscle tears, are tied directly to the forces and torques we’ve examined. Strength training, physical therapy, and even ergonomic design rely heavily on these biomechanical principles to improve performance and reduce injury.