# Different types of linkages

## Types of Linkages explained

Before reading this article, you may also enjoy our Basics of linkages Article here

A linkage is a mechanism formed by connecting two or more levers together. Linkages can be designed to change the direction of a force or make two or more objects move at the same time. Many different fasteners are used to connect linkages together yet allow them to move freely such as pins, end-threaded bolts with nuts, and loosely fitted rivets. There are two general classes of linkages: simple planar linkages and more complex specialized linkages; both are capable of performing tasks such as describing straight lines or curves and executing motions at differing speeds. The names of the linkage mechanisms given here are widely but not universally accepted in all textbooks and references. Linkages can be classified according to their primary functions:

• Function generation: the relative motion between the links connected to the frame
• Path generation: the path of a tracer point
• Motion generation: the motion of the coupler link

## Simple Planar Linkages

Four different simple planar linkages shown below are identified by function:

• Reverse-motion linkage, Fig a below can make objects or force move in opposite directions; this can be done by using the input link as a lever. If the fixed pivot is equidistant from the moving pivots, output link movement will equal input link movement, but it will act in the opposite direction. However, if the fixed pivot is not centered, output link movement will not equal input link movement. By selecting the position of the fixed pivot, the linkage can be designed to produce specific mechanical advantages. This linkage can also be rotated through 360°.
• Push-pull linkage, Fig. b, can make the objects or force move in the same direction; the output link moves in the same direction as the input link. Technically classed as a four-bar linkage, it can be rotated through 360° without changing its function.

• Parallel-motion linkage, Fig. C, can make objects or forces move in the same direction, but at a set distance apart. The moving and fixed pivots on the opposing links in the parallelogram must be equidistant for this linkage to work correctly. Technically classed as a four-bar linkage, this linkage can also be rotated through 360° without changing its function. Pantographs that obtain power for electric trains from overhead cables are based on parallel-motion linkage. Drawing pantographs that permit original drawings to be manually copied without tracing or photocopying are also adaptations of this linkage; in its simplest form it can also keep tool trays in a horizontal position when the toolbox covers are opened.

• Bell-crank linkage, Fig. D, can change the direction of objects or force by 90°. This linkage rang doorbells before electric clappers were invented. More recently this mechanism has been adapted for bicycle brakes. This was done by pinning two bell cranks bent 90° in opposite directions together to form tongs. By squeezing the two handlebar levers linked to the input ends of each crank, the output ends will move together. Rubber blocks on the output ends of each crank press against the wheel rim, stopping the bicycle. If the pins which form a fixed pivot are at the midpoints of the cranks, link movement will be equal. However, if those distances vary, mechanical advantage can be gained.

Four-bar linkages share common properties: three rigid moving links with two of them hinged to fixed bases which form a frame. Link mechanisms are capable of producing rotating, oscillating, or reciprocating motion by the rotation of a crank. Linkages can be used to convert:

• Continuous rotation into another form of continuous rotation, with a constant or variable angular velocity ratio
• Continuous rotation into oscillation or continuous oscillation into rotation, with a constant or variable velocity ratio
• One form of oscillation into another form of oscillation, or one form of reciprocation into another form of reciprocation, with a constant or variable velocity ratio

There are four different ways in which four-bar linkages can perform inversions or complete revolutions about fixed pivot points. One pivoting link is considered to be the input or driver member and the other is considered to be the output or driven member. The remaining moving link is commonly called a connecting link. The fixed link, hinged by pins or pivots at each end, is called the foundation link.

Crank-rocker mechanism, Fig above, demonstrates the second inversion. The shortest link AB is adjacent to AD, the foundation link. Link AB can make a full 360revolution while the opposite link CD can only oscillate and describe an arc.

Double-rocker mechanism, below, demonstrates the third inversion. Link AD is the foundation link, and it is opposite the shortest link BC. Although link BC can make a full 360revolution, both pivoting links AB and CD can only oscillate and describe arcs.

The fourth inversion is another crank-rocker mechanism that behaves in a manner similar to the mechanism shown below

## Straight-Line Generators

Linkages that are capable of describing straight lines are known as straight-line generators. These linkages are important components in various types of machines, particularly machine tools. The dimensions of the rigid links play an important role in ensuring that these mechanisms function correctly.

One example of a straight-line generator is Watt's straight-line generator. This linkage is able to describe a short vertical straight line. It consists of equal length links AB and CD, which are hinged at A and D, respectively. The midpoint E of connecting link BC traces a figure eight pattern over the full mechanism excursion, but a straight line is traced in part of the excursion because point E diverges to the left at the top of the stroke and to the right at the bottom of the stroke. Scottish instrument maker James Watt used this linkage in a steam-driven beam pump around 1769, and it was also a prominent mechanism in early steam-powered machines.

Another example of a straight-line generator is the Scott Russell straight-line generator. This linkage can also describe a straight line. Link AB is hinged at point A and pinned to link CD at point B. Link CD is hinged to a roller at point C, which restricts it to horizontal oscillating movement.

Rotary/Linear Linkages, also known as Slider-crank mechanisms, are mechanical devices that convert rotary motion into linear motion or vice versa. They consist of three links - a rotating crank, a sliding connecting rod, and a sliding block or piston.

The crank is a rotating lever that is attached to a motor or an engine, while the connecting rod is a rigid link that slides back and forth within a channel or a slot. The sliding block or piston is attached to the end of the connecting rod and moves in a linear direction.

As the crank rotates, it moves the connecting rod back and forth, causing the sliding block or piston to move in a linear direction. This linear motion can be used to perform work, such as driving a pump, lifting a load, or moving a conveyor belt.

The opposite is also true - linear motion can be converted into rotary motion. When a force is applied to the sliding block or piston, it moves the connecting rod back and forth, causing the crank to rotate. This rotary motion can be used to power a generator, a saw blade, or a grinding wheel.

Slider-crank mechanisms are widely used in various applications, including engines, pumps, compressors, and many types of manufacturing equipment. They are efficient, reliable, and easy to maintain, making them an essential component of many industrial processes.

## How a Scotch-yoke mechanism works

A Scotch-yoke mechanism is a type of reciprocating motion mechanism that converts rotary motion into linear motion. It is named after the Scottish engineer James Watt who used it in steam engines.

The mechanism consists of a rotating crankshaft with a pin, called the yoke, attached to it. The yoke moves back and forth along a straight line, guided by a slot in a sliding block or slider. The slider is connected to a piston or other device that requires linear motion.

As the crankshaft rotates, the yoke moves back and forth in a straight line, pushing and pulling the slider along with it. The motion of the slider can be used to perform work, such as pumping fluids or moving objects along a track.

The key advantage of the Scotch-yoke mechanism is that it provides a smooth, constant velocity motion to the slider, unlike other mechanisms that can produce jerky or uneven motion. However, it also has some disadvantages, such as high friction and wear due to the sliding contact between the yoke and the slider, and the need for precise alignment of the yoke and the slider to avoid binding.

Overall, the Scotch-yoke mechanism is a simple and effective way to convert rotary motion into linear motion, and it has been used in a wide range of applications, including engines, pumps, and manufacturing equipment.

## How a Rotary-to-linear mechanism works

A rotary-to-linear mechanism is a type of mechanism that converts rotational motion into linear motion. This can be achieved through a variety of mechanisms, each with their own unique advantages and disadvantages.

One common type of rotary-to-linear mechanism is the screw mechanism, which consists of a screw and a nut. The screw has a threaded shaft that is rotated by a motor or other source of rotary motion. The nut is threaded onto the screw and moves along the length of the screw as it rotates. This linear motion can be used to perform work, such as moving a platform or lifting a load.

Another type of rotary-to-linear mechanism is the crankshaft mechanism, which is commonly used in engines. The crankshaft has a series of cranks or journals that are offset from the centerline of the shaft. As the shaft rotates, the cranks push and pull connecting rods that are attached to pistons or other devices that require linear motion.

Yet another type of rotary-to-linear mechanism is the cam mechanism, which uses a rotating cam to produce linear motion. The cam has a non-circular shape that causes a follower, such as a roller or a lever, to move in a linear path as the cam rotates. This can be used to perform a variety of functions, such as opening and closing valves or moving a platform along a track.

Overall, rotary-to-linear mechanisms are essential components in many machines and devices. The choice of mechanism depends on factors such as the required amount of linear motion, the speed and accuracy of the motion, and the available space and power sources.

To understand the other classes of levers, we have created some blog posts on those shown below: