Muscle Torque

Muscles are a Simple Machine

Muscles are examples of Simple Machines.

With a lever, you can either increase the force of the movement, its speed, or its range of motion; but you can’t do all three at the same time. Levers are about tradeoffs; you trade one benefit for another. A lever is composed of a fulcrum, effort, and load.

1. Fulcrum: the point at which the lever rests and pivots.
2. Effort (input force): characterized by the amount of work the operator does and is calculated as the force used multiplied by the distance over which the force is used.
3. Load (output force): the object being moved or lifted; sometimes referred to as resistance.

There are three classes of levers: First, Second, and Third. There are very few first and second-class levers in the human body.

Three lever classes StudySmarter Originals

All skeletal muscles provide stability and produce movement in the human body by acting as the force or effort applied to the levers of our bones, and by using opposing forces to achieve a mechanical advantage. To put it another way, muscles move bones around joints.

Muscle Torque Definition

To understand how torque relates to muscles, let's take a look at torque in the general sense. Torque is a measure of how much a force acting on an object causes that object to rotate. The equation for torque is:

$$T=rf\sin\phi$$

where \(t\) is the torque, \(r\) is the radius, \(f\) is the force and \(\phi\) is the angle between the force and the arm.

Muscles create the torques that turn our limbs. When a muscle contracts it pulls on its point of attachment, along the line of action.

Forces and Torques in Muscles and Joints

Muscle torque is the force applied by the muscles through a moment arm. In order to have muscle torque, the joint is needed. The joint, when at different angles will produce variations of muscle torque. Since our muscles can only contract, they occur in pairs throughout our body. In the arm, the bicep muscle is a flexor— that is, it closes the limb. The tricep muscle is an extensor that opens the limb. This configuration is typical of skeletal muscles, bones, and joints in humans. The reason most skeletal muscles exert larger forces than limbs is that most of our muscles are attached to bones via tendons near joints, causing these systems to have mechanical advantages.

Muscular Torques

Torque is crucial for human movement because it is what creates movement at our joints. The moment arm is crucial and some key things to remember about the moment arm are:

The angle of pull is the angle between the line of pull and the muscle and bone on which it inserts (angle toward the joint). It is the angle formed between the line of pull of a muscle and the longitudinal axis of the bone in which the muscle is acting.

• When there is any degree of motion in the joint, the angle of pull changes.
• The joint movements and insertion angles involve mostly small angles of pull.
• The line of pull is usually indicated by the joint angle.
• The angle of pull affects the strength of muscle action; at only certain angles of pull can a muscle exert maximal Tension.

• Variable resistance exercise machines compensate for variations in muscular tension at different joint angles.

The angle of pull of a bicep at the joint showing stabilizing and rotary force components StudySmarter Originals

Since the muscle angle of pull determines the type of movement at the joint, by learning where the muscle originates and inserts, you can determine the angle of pull and determine the action of the muscle.

There are 3 main components of force to the angle of pull:

• Rotary component: a force of a muscle contributing to bone's movement around a joint axis; greatest when muscles angle of pull is perpendicular to bone (ie: 90 degrees).
• Stabilizing component: a degree of parallel forces generated on the lever (bone and joint) when the muscle's angle of pull is less than 90 degrees.
• Dislocating component: a degree of parallel forces generated on the lever (bone and joint) when the muscle's angle of pull is greater than 90 degrees.

If you want to produce the peak torque from a muscle, the joint must be positioned so that the muscle being worked has a 90° angle of pull on the extremity.

Now, let's try a problem where we calculate muscle torque.

Muscle torque equation

We can use this equation for the torque on a muscle when the forces are perpendicular to the moment arm:

$$T=M_{\text{Arm}}f$$

Torque = Force multiplied by moment arm

Step 1:

Before you sum up the torques, you must identify the forces that have a moment arm and can create a torque.

To do this, go through the problem, identify each force, and give it a label to stay on track with the equation.

For this problem, let's say:

• The weight of the dumbbell can be labeled W_D (where D stands for dumbbell).

• The weight of the forearm/hand segment can be labeled W_S (where S stands for segment).

• The muscle force can be labeled F_M (where M stands for muscle).

Weight is a force that always acts downward. Use a plus sign (+) for the upward direction, and a minus sign (–) for the downward direction. Weights are applied at the center of gravity of a body, and the location of the center of gravity for both the segment and the dumbbell weight are given.

Step 2:

Create a table listing what you'll use to calculate the torques, and fill in the known information from the word problem, sort of like this:

Tips:

Remember to list weights as negative forces, and the moment arm for each force is on the same side of the elbow joint axis, so set them all as positive.

The moment arms for the segment weight and the dumbbell weight are the distance of each center of gravity from the elbow axis because the forearm/hand is in a horizontal position.

The torque created by each force is calculated as a product of the force and moment arm.

The weights (segment and dumbbell) create negative torques, so it's important to list the direction, and magnitude of the torque in the table.

Step 3:

Next, use the equation:

\[\sum\,T=0\]

To solve for the torque created by the muscle \(T_M\).

Expand the equation to list all of the torques: \(T_M+T_D+T_S=0\).

Isolate for the unknown muscle torque:

$$T_M=T_D-T_S.$$Step 4:

Fill in known values from the table you created above and then solve the problem: $$T_M=(-170\,\mathrm{Nm})-(-3.9\,\mathrm{Nm})=173.9\,\mathrm{Nm}$$The muscle must create a torque of \(173.9\, \mathrm{Nm}\) which is opposite in direction to the torques created by segment and dumbbell weights, to prevent angular acceleration.

Step 5:

Calculate the muscle force \((F_M)\) using this equation: \[T_M=F_M\,\times\,M_{\text{Arm}}\]

Isolate for \(F_M\)

Rearrange the equation: $$F_{\mathrm M}=\frac{T_{\mathrm M}}{M_{\mathrm{Arm}}}=\frac{173.9\;\mathrm{Nm}}{0.05\;\mathrm m}=3\,478\;\mathrm N$$

Muscle torque required to prevent rotation is \(3\,478\,\mathrm{N}\).