## Linkages and levers - The basics

Mechanical linkages have the ability to convert a type of force into a different one, as well as convert direction into another direction or movement.

When two or more levers are interconnected, they form what is called a linkage. A linkage is a mechanism that transmits motion and force between the levers. By joining levers together, we can create a variety of different linkages with different properties and applications.

Simple linkages are one type of linkage that can be created by joining levers together. These linkages are designed to change the direction of motion and the amount of force applied. For example, if we connect two levers with a pivot point, we can create a basic scissor mechanism. As we squeeze the two levers together, the motion is transferred to the pivot point, which causes the scissor blades to move in opposite directions. This simple linkage allows us to apply force in one direction and convert it into a different direction of motion.

Other types of linkages can be designed to amplify or reduce the amount of force applied. By changing the length and positioning of the levers in the linkage, we can control the mechanical advantage of the system. This can be useful in a wide range of applications, from simple machines like scissors to complex machinery used in manufacturing and engineering.

reverse motion refers to the movement of an output element in the opposite direction to the input element. This occurs when the input and output elements are connected by a linkage that changes the direction of motion.

For example, consider a simple lever connected to a linkage that changes the direction of motion. If we push down on the lever, the linkage will transmit the motion to the output element, causing it to move in the opposite direction. This is reverse motion because the output element moves in the opposite direction to the input element.

Reverse motion can be useful in many applications where we need to transmit motion and force in a different direction from the input. Linkages can be designed to create different types of reverse motion, including parallel motion and crank motion. Parallel motion linkages keep the output element parallel to the input element, while crank motion linkages convert rotary motion into linear motion.

Understanding reverse motion and how it can be created using linkages is important for designing and engineering machines and mechanical systems. By using linkages to control the direction and amount of motion and force, we can create efficient and effective machines that meet a wide range of needs and applications.

## Parallel motion or push/pull linkages

A parallel motion linkage, also known as a push-pull linkage, is a type of mechanical linkage that is designed to maintain a constant distance between the input and output elements. This means that when the input element is moved, the output element moves in the opposite direction while remaining parallel to the input element.

Push-pull linkages are often used in applications where a linear motion needs to be transmitted without any change in orientation. One common example of this is in the operation of overhead doors or gates. A push-pull linkage is used to connect the door or gate to the motor, so that when the motor is activated, the door or gate moves in a straight line without tilting or rotating.

Push-pull linkages can be designed using a variety of mechanisms, including levers, bell cranks, and rods. In general, these linkages are most effective when they are designed with a balanced layout, meaning that the input and output elements are equally spaced from the pivot points of the linkage. This helps to ensure that the output motion is smooth and consistent.

Overall, push-pull or parallel motion linkages are an important tool for engineers and designers who need to create linear motion in a wide range of applications. They are relatively simple to design and manufacture, and can be adapted to meet a variety of needs and requirements.

A bell crank linkage is a type of mechanical linkage that is used to transmit motion and force around corners or obstacles. It consists of two arms that are connected at a pivot point, with one arm serving as the input element and the other arm serving as the output element. The pivot point is often located at the corner of the obstacle that the linkage needs to bypass.

Bell crank linkages are commonly used in machinery and mechanical systems where space is limited or where motion needs to be transmitted around obstacles. They are especially useful in applications where the input and output elements need to be oriented in different directions.

One common example of a bell crank linkage is in the steering system of a car. The steering column rotates a horizontal shaft that is connected to a bell crank, which then transmits the motion around a corner to another bell crank that is connected to the steering arms on the front wheels. This allows the wheels to turn left or right in response to the motion of the steering column.

Bell crank linkages can be designed in a variety of shapes and sizes to meet different needs and requirements. They can be used to transmit motion and force over short distances or over longer distances with multiple pivot points. Overall, bell crank linkages are an important tool for engineers and designers who need to create motion and force transmission around obstacles or in confined spaces.

A crank and slider linkage is a type of mechanical linkage that is used to convert rotary motion into reciprocating linear motion. The linkage consists of a crank, which is a rotating lever, and a slider, which is a block that moves back and forth in a straight line.

The crank and slider linkage works by connecting the crank to the slider with a connecting rod. As the crank rotates, it pushes and pulls the connecting rod, which in turn moves the slider back and forth in a straight line.

Crank and slider linkages are commonly used in machinery and mechanical systems where a reciprocating motion is needed. One common example of a crank and slider linkage is in the engine of a car. The pistons in the engine are connected to the crankshaft with connecting rods, which convert the rotary motion of the crankshaft into reciprocating motion of the pistons.

Crank and slider linkages can also be used in a wide range of other applications, such as in pumps, compressors, and industrial machinery. They can be designed with different crank and slider configurations to achieve different stroke lengths, speeds, and force outputs.

Overall, the crank and slider linkage is an important tool for engineers and designers who need to create linear motion from rotary motion. By connecting a crank to a slider with a connecting rod, this linkage allows for the efficient conversion of rotary motion into reciprocating linear motion.

A treadle linkage is a type of mechanical linkage that is used to convert the linear motion of a treadle, or foot pedal, into a different type of motion, such as rotational or reciprocating motion. The linkage consists of a series of levers and pivots that transmit the motion of the treadle to the output element.

Treadle linkages are commonly used in a variety of applications, such as in sewing machines, looms, and other types of machinery where foot power is used to operate the machine.

The basic principle of a treadle linkage is that when a foot pedal is depressed, it pushes down on a connecting rod or other type of input element. This input element then transmits the motion to a series of levers and pivots, which convert the linear motion of the treadle into a different type of motion.

One common example of a treadle linkage is in a sewing machine. When the operator depresses the foot pedal, it causes a connecting rod to move back and forth. This connecting rod is connected to a lever, which pivots and transmits the motion to a rotating shaft. The rotating shaft then drives the needle up and down, allowing the operator to sew fabric together.

Treadle linkages can be designed in a variety of configurations to achieve different types of motion and force outputs. They can also be designed with different ratios of input to output motion, allowing the operator to control the speed and intensity of the output motion.

When using levers, it is important to understand the angles between the lever arms and the direction of the applied force, as well as the position of the fulcrum. The angle between the lever arms and the direction of the applied force is known as the mechanical advantage angle, and it can have a significant impact on the effectiveness and efficiency of the lever system.

In general, the mechanical advantage of a lever system is determined by the ratio of the length of the lever arms on either side of the fulcrum. A longer lever arm will provide a greater mechanical advantage, allowing a smaller force to be used to achieve the same amount of work. However, the mechanical advantage angle also plays a role in the effectiveness of the lever system.

When the mechanical advantage angle is too small, the lever system may not be able to produce enough force to overcome the resistance being acted upon. This can result in the lever system being ineffective or inefficient. On the other hand, when the mechanical advantage angle is too large, the lever system may require a greater force input than is necessary, leading to wasted energy and effort.

Understanding the angles in place for each arrangement of levers allows engineers and designers to optimize the mechanical advantage of the lever system, maximizing its efficiency and effectiveness. By carefully selecting the position of the fulcrum and the length of the lever arms, they can design lever systems that are tailored to the specific needs and requirements of the application. This can help to reduce the amount of force required to perform a task, conserve energy, and improve overall performance.

In the image above, the top angle is 30°, and therefore the alternate internal angle at the bottom is also 30°

In the diagram below, angles A, B and C can be calculated for a parallel linkage

•  Angle A above = 115 degrees, and it matches 115 degrees on the Z angle.
• A and B both sit on a horizontal line, so 115 degrees + B = 180 degrees.
• B and C match on a Z angle, so B and C are both 65 degrees.

To view our blog post on the different types of linkages, clock on the link below