Explore the mechanics behind graphical integration with the MOC-237895 Mechanical Integraph Plotter Building Blocks. Designed and authorized by Nico71, this 688-piece model recreates a 19th-century mathematical instrument originally developed for plotting the integral of a graphically defined function.

Using only mechanical linkages, sliding carriers, rotating arms, and a tangent wheel, the model translates the movement of an input stylus into a second plotted curve. No electric power is required, making the relationship between motion, slope, and integration directly visible through the mechanism itself.

A Mechanical Calculus Instrument

The integraph was developed as a practical way to obtain the integral of a function from a drawn curve.

Instead of calculating numerically, the machine converts the geometry of the input curve into the motion of an output pencil, producing a new curve that represents its integral.

X-Axis & Y-Axis Input Movement

The wheeled chassis moves along the x-axis, while the input stylus travels vertically along the y-axis.

As the stylus follows the original curve, its position changes the angle of the main orientation arm inside the machine.

Parallelogram Linkage System

A sliding carrier and parallelogram linkage transfer the angle of the main arm toward the tangent-wheel assembly.

This arrangement keeps key beams parallel while separating different movements, allowing translation and rotation to interact without becoming mechanically locked together.

Tangent Wheel Integration Mechanism

At the heart of the machine is a freely moving tangent wheel.

When the wheel is aligned with the y-axis, the output carrier remains stationary. When the wheel rotates to an angle, it forces the carrier sideways as the chassis moves forward.

Because that angle is determined by the input y-value, the output pencil follows a curve whose slope corresponds to the original function.

Visible Calculus in Motion

The principle behind the machine is based on a fundamental relationship in calculus: the slope of an integral curve corresponds to the value of the original function.

This means the model physically demonstrates integration through geometry and motion rather than electronics or software.

Purely Mechanical Operation

The complete process is driven by wheels, sliders, carriers, linkages, and rotating elements.

There are no electric motors required, making the model particularly useful as a hands-on demonstration of mechanical computation.

Historical Engineering Applications

Real integraphs were used in applied mathematics and engineering for tasks such as:

• Area calculations
• Centers of gravity
• Moments of inertia
• Structural loads and resistance
• Differential equations
• Electromagnetism
• Shipbuilding
• Optics
• Motion and velocity analysis

Unlike a planimeter, which mainly provides the area beneath a curve, an integraph can generate the actual integral curve for further analysis.

From the Designer

Nico71 created MOC-237895 as a mechanical recreation of the classic integraph associated with Abdank-Abakanowicz.

The main challenge was not simply reproducing its appearance, but recreating the complete movement chain that converts stylus displacement into arm rotation, transfers that angle through the parallelogram mechanism, and finally guides the tangent wheel and output pencil.

The resulting model turns an abstract mathematical idea into a physical machine where the integration process can be watched as it happens.

A Mechanical Mathematics Display

With 688 pieces, a fully mechanical plotting system, visible linkages, and a genuine mathematical operating principle, MOC-237895 is an unusual display and educational build for engineering enthusiasts, mathematics fans, mechanical-computation collectors, and builders interested in historical scientific instruments.