Integraph : Graphic Planimeter

An Integraph is an instrument used in mathematics for plotting the integral of a graphically defined function.


How does it work :

Trolley 1 move from left to right thanks to the input stylus and slides, the main arm is connected to the trolley 1 thanks to a slide. Then the angle of the arm depends on abscissa position of the input stylus. The trolley 2 move on the main arm. The parallelogram is connected to the trolley 2. The parallelogram is connected to the tangent wheel. Thefore the angle of the wheel depends on the angle of parallelogram. Consequently, the angle of the tangent wheel depends on abscissa position of the input stylus.
The parallelogram enables the tangent wheel to always have the same angle, despite the position of the trolley. If the tangent wheel has the same angle of the displacement : trolley 3 doesn’t move. If the tangent wheel hasn’t the same angle : trolley 3 moves. The conjonction of the tangent wheel and  the displacement of the troley 3 is the trick to plot the integral.
To resume :  The conjonction enables the device to plot integral because the wheel is always tangent to the curve and the angle depends on the abscissa position of the input stylus.

The result : y=x and trignometric circle integral.

The building instructions are available. You can watch them by browsing my website or

Download the Zip Archive of the Planimeter Integraph’s instructions, 4 mo, ZIP.

Designed in 2011.

(8) Comments

    hey i made 5 hours of trying to find ll of the pieces and the fact of biulding it and the prt that has the wheel and connects to the stylus will N O T work when i move it in ANY way i just popps off and breaks so please help me is the black part a wieght, does it need to be E X A C T L Y the sa,e as urs pls help me

    Désolé non, ce n’est pas vraiment une notice mais plus des photos de démontage, donc pas de liste des pièces.


    Un résumé des pièces nécessaires au montage est-il disponible comme pour le planimètre orthogonal?

    Merci d’avance.


    In School, wie learnd last month about functions. The integraph is a very gold help! Thank you, Nico71! 🙂

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