Types of Mechanical Linkages: Complete Guide to Linkage Mechanisms

What Are Mechanical Linkages?

A mechanical linkage is a mechanism formed by connecting two or more rigid links together with joints (pins, pivots, or sliders) to transmit force and motion in a controlled way. Linkages can change the direction of a force, amplify or reduce it, make multiple objects move simultaneously, or convert between different types of motion — rotary, linear, and oscillating.

Linkages are fundamental to mechanical engineering and appear everywhere: in engines, industrial machinery, robotics, vehicle steering and suspension systems, aircraft control surfaces, and in the mounting systems for linear actuators. Understanding the different types of linkages is essential for designing efficient mechanisms and choosing the right actuator configuration for any application.

Before reading further, you may also want to review our Basics of Linkages: Fundamentals article for an introduction to linkage terminology and principles.

Linkages are classified by their primary function:

• Function generation — controlling the relative motion between links connected to the frame
• Path generation — guiding a tracer point along a specific path (straight line or curve)
• Motion generation — moving a coupler link through a defined sequence of positions

There are two general classes: simple planar linkages (reverse-motion, push-pull, parallel-motion, bell-crank) and specialized linkages (four-bar inversions, straight-line generators, slider-crank, Scotch-yoke, cam-follower, and screw mechanisms).

All Types of Linkages at a Glance

The table below summarizes every major linkage type covered in this guide, including what each one does, how many links and joints it has, and where it’s commonly used.

Simple Planar Linkages

The four simplest planar linkages are the building blocks of more complex mechanisms. Each performs a single fundamental motion transformation.

Reverse-Motion Linkage

A reverse-motion linkage (Fig. a) makes objects or forces move in opposite directions. It works by using the input link as a lever around a fixed pivot. If the fixed pivot is equidistant from both moving pivots, the output movement equals the input movement but in the opposite direction. If the fixed pivot is off-center, the linkage produces mechanical advantage — the output moves a different distance than the input, amplifying or reducing the force. This linkage can rotate through a full 360°.

Push-Pull Linkage

A push-pull linkage (Fig. b) makes objects move in the same direction. The output link tracks the input link’s movement. Technically a four-bar linkage, it can rotate through 360° without changing its function. Push-pull linkages are used wherever two components need to move together in parallel.

Parallel-Motion Linkage

A parallel-motion linkage (Fig. c) moves objects in the same direction while maintaining a fixed distance between them. The moving and fixed pivots on opposing links must be equidistant for the mechanism to work correctly — forming a parallelogram. This is the principle behind pantographs used to pick up electrical power for trains from overhead cables, drawing pantographs for copying diagrams, and fold-out tool trays that stay horizontal as a toolbox lid opens. This linkage also rotates through 360°.

Bell-Crank Linkage

A bell-crank linkage (Fig. d) redirects force or motion by 90 degrees. Named after the mechanical doorbells it originally powered, the bell crank consists of two arms joined at a right angle with a fixed pivot at the bend. When force is applied to one arm, the other arm moves perpendicular to it.

The most familiar modern application is bicycle rim brakes: two bell cranks bent 90° in opposite directions are pinned together to form tongs. Squeezing the brake levers (input) pushes the rubber pads (output) inward against the wheel rim. If the pivot is at the midpoint of the cranks, movement is equal on both sides. Moving the pivot off-center creates mechanical advantage.

Four-Bar Linkages and Their Inversions

Four-bar linkages are the most versatile and widely used class of linkage mechanisms. Despite the name, they have three moving links and one fixed link (the frame), connected by four pin joints. The configuration of link lengths determines which of the four possible inversions (motion behaviors) the linkage produces.

Four-bar linkages can convert:

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

The three moving links are called the input link (driver), the output link (driven), and the connecting link (coupler). The fixed link is the foundation link or frame.

Crank-Rocker Mechanism (Second Inversion)

In the crank-rocker mechanism, the shortest link (AB) is adjacent to the foundation link (AD). Link AB can make a full 360° revolution while the opposite link (CD) can only oscillate through an arc. This is the most common four-bar linkage configuration and is found in windshield wipers, rocking toys, and many industrial machines.

Double-Rocker Mechanism (Third Inversion)

In the double-rocker mechanism, the foundation link (AD) is opposite the shortest link (BC). Although the coupler link BC can make a full 360° revolution, both pivoting links (AB and CD) can only oscillate and describe arcs. Neither the input nor output link completes a full revolution.

The fourth inversion produces another crank-rocker mechanism that behaves similarly to the second inversion but with different link proportions.

Straight-Line Generators

Straight-line generators are linkages designed to trace a straight-line path from rotary input. They are critical components in machine tools, precision measurement instruments, and any application where accurate linear guidance is needed without rails or slides.

Watt’s Straight-Line Generator

Watt’s linkage consists of two equal-length links (AB and CD) hinged at points A and D respectively. The midpoint E of the connecting link BC traces a figure-eight pattern over the full excursion, but traces a nearly perfect straight line through the middle portion of the stroke. Point E diverges slightly left at the top of the stroke and right at the bottom.

Scottish instrument maker James Watt used this linkage in a steam-driven beam pump around 1769. It was one of the most important mechanisms of the early Industrial Revolution, enabling steam engines to drive piston rods in a straight line without requiring precision-ground slide rails.

Scott Russell Straight-Line Generator

The Scott Russell linkage produces straight-line motion using a different approach. Link AB is hinged at point A and pinned to link CD at point B. Link CD is constrained to horizontal movement by a roller at point C. As point A oscillates, point D traces a vertical straight line.

Other Classical Straight-Line Generators

Several other linkages have been developed to produce straight-line motion, each with different trade-offs between accuracy, range of motion, and mechanical complexity.

Slider-Crank Mechanisms (Rotary/Linear Linkages)

Slider-crank mechanisms convert rotary motion into linear reciprocating motion, or vice versa. They consist of three links: a rotating crank, a connecting rod, and a sliding piston or block.

As the crank rotates, it pushes and pulls the connecting rod, driving the slider back and forth in a straight line. This linear motion can drive pumps, lift loads, or move conveyor belts. The reverse also works — applying force to the slider (as in an internal combustion engine where expanding gas pushes a piston) rotates the crank, powering a generator or driveshaft.

Slider-crank mechanisms are among the most widely used linkages in engineering, found in internal combustion engines, reciprocating compressors, hydraulic pumps, stamping presses, and many types of manufacturing equipment.

The screw mechanism inside a linear actuator is a specialized form of rotary-to-linear conversion — a motor spins a lead screw or acme screw, and a nut riding on the screw threads converts that rotation into precise linear extension and retraction.

Scotch-Yoke Mechanisms

A Scotch-yoke mechanism is a type of reciprocating motion linkage that converts rotary motion into smooth, sinusoidal linear motion. It consists of a rotating crankshaft with a pin (the yoke) that rides in a slot cut into a sliding block. As the crankshaft rotates, the yoke pushes the slider back and forth along a straight line.

The key advantage of the Scotch yoke over a slider-crank is that it produces true sinusoidal motion with smooth, constant-velocity characteristics at mid-stroke. This makes it ideal for applications requiring smooth reciprocation, such as pumps, valve actuators, and vibration testing machines.

The trade-offs are higher friction and wear at the yoke-to-slot contact, and the need for precise alignment to avoid binding. Despite these limitations, the Scotch yoke remains widely used in Bourdon tube pressure gauges, pneumatic actuators, and some high-performance racing engines.

Rotary-to-Linear Mechanisms

Rotary-to-linear mechanisms are a broad category of linkages and devices that convert rotational motion into straight-line motion. The slider-crank and Scotch yoke covered above are two examples, but several other mechanisms achieve this conversion through different principles:

Screw mechanisms use a threaded shaft rotated by a motor. A nut threaded onto the screw translates along its length as the screw turns. Screw mechanisms provide high mechanical advantage and precise positioning, making them the operating principle inside most electric linear actuators. Lead screws, ball screws, and acme screws are all variants of this mechanism.

Cam mechanisms use a rotating cam with a non-circular profile to push a follower (roller or lever) along a programmed path. By shaping the cam profile, the designer can produce virtually any motion pattern — dwell periods, quick returns, constant velocity segments. Cam mechanisms are used in engine valve trains, packaging equipment, and automated assembly machines.

Rack and pinion mechanisms convert rotation of a gear (pinion) into linear motion of a toothed bar (rack). This is the mechanism behind most automotive steering systems and is also used in CNC machines, 3D printers, and linear positioning stages.

Grashof’s Law: Predicting Four-Bar Linkage Behavior

Before building a four-bar linkage, you need to know which type of motion it will produce. Grashof’s law provides a simple test based on link lengths:

s + l ≤ p + q

Where s is the shortest link, l is the longest link, and p and q are the other two links. If this inequality holds:

• The shortest link can make a full revolution relative to any adjacent link
• If the shortest link is the crank (adjacent to frame) → crank-rocker
• If the shortest link is the frame → double-crank (drag-link)
• If the shortest link is the coupler → double-rocker

If s + l > p + q, the linkage is a non-Grashof linkage and no link can make a complete revolution — all links can only oscillate.

Understanding Grashof’s law is essential for designing linkages that behave as intended, especially when connecting a linear actuator to a mechanism where the actuator must travel through a full stroke without hitting a dead point.

Linkages and Linear Actuators

Linear actuators produce straight-line force and motion, but many real-world applications require the force to be redirected, amplified, or applied through an arc. This is where linkages become essential. Every actuator-powered lid, hatch, panel, or platform is a linkage problem — the actuator connects to the load through a lever, crank, or linkage system that determines the force, stroke, and motion profile.

Common linkage configurations used with linear actuators include:

• First-class lever — the pivot is between the actuator (effort) and the load, like a seesaw. Used in counterbalanced mechanisms and rocking platforms. Calculate force and stroke with our First Class Lever Calculator.
• Second-class lever (hatch/lid) — the load is between the pivot and the actuator. This is the most common actuator linkage — opening hatches, lids, trap doors, and pop-top camper roofs. The lever amplifies the actuator’s force based on mounting geometry. Use our Second Class Lever Calculator or Lid & Hatch Calculator to size actuators for this configuration.
• Third-class lever — the actuator is between the pivot and the load. This trades force for speed and range of motion — the load moves farther and faster than the actuator, but requires more actuator force. Calculate with our Third Class Lever Calculator.
• Bell-crank redirect — a bell-crank linkage redirects actuator force 90° for tight-space installations where the actuator cannot be mounted in line with the load direction.
• Parallel-motion linkage (scissor lift) — keeps a platform level as actuators raise or lower it, used in scissor lifts, adjustable workstations, and vehicle platforms. Try our Scissor Lift Calculator.
• Compound lever — multiple levers in series multiply the actuator’s mechanical advantage for very heavy loads. See our Compound Lever Calculator.

The screenshot below shows our interactive second-class lever calculator — enter your panel weight, hinge position, and actuator mounting point, and the calculator computes the exact force and stroke required in real time.

The same linkage principles apply to any hinged panel powered by an actuator. The image below shows a campervan pop-top roof configured as a second-class lever — the hinge is at one edge, the roof weight is the load, and the actuator pushes from below. Getting the actuator mounting position right is critical for force and stroke.

For scissor-lift linkages, our calculator handles the more complex parallel-motion geometry where the actuator drives crossing arms that raise a platform vertically while keeping it level.

The choice of linkage directly affects the actuator’s force requirement, stroke length, and mounting geometry. A well-designed linkage can let you use a smaller, less expensive actuator to move a heavier load — or allow an actuator to operate in a space where direct-push mounting isn’t possible.

Choosing an Actuator for Your Linkage

Once you’ve determined the force and stroke your linkage requires, select an actuator that exceeds the calculated peak force by at least 1.5× for safety margin. FIRGELLI offers actuators across a wide range of force, speed, and stroke combinations:

• All Linear Actuators — browse the full range by force, stroke, and speed
• Bullet 50 Cal Series — heavy-duty, IP66, built-in feedback, ideal for outdoor and camper applications
• Super Duty Actuators — highest force ratings for heavy lids, hatches, and industrial linkages
• Feedback Rod Actuators — position feedback for precise linkage control and synchronization

Related Engineering Calculators and Guides

Use these free tools and references to design linkage-based mechanisms with linear actuators:

• Basics of Linkages: Fundamentals — introduction to linkage terminology, degrees of freedom, and design principles
• First Class Lever Calculator — calculate actuator force and stroke for first-class lever mechanisms
• Second Class Lever Calculator — force and stroke for second-class levers (lids, hatches, wheelbarrow-type mechanisms)
• Third Class Lever Calculator — force and stroke for third-class levers (speed amplification, fishing-rod-type mechanisms)
• Compound Lever Calculator — cascaded levers for high mechanical advantage
• Lid & Hatch Actuator Calculator — size actuators for hinged lids, hatches, and pop-top roofs
• Scissor Lift Calculator — force and stroke for scissor-lift mechanisms
• Full Calculator Suite — all FIRGELLI engineering calculators in one place
• Mastering Mechanical Advantage — comprehensive guide to levers, pulleys, gears, and hydraulics