When tracing point A is moved along curve y=f(x), lever 1 is turned about point F by which it is pivoted to slide 2. This moves slide 2 along guides 3 parallel to axis 4. Simultaneously, lever 1, through turning pair B and slider 6, moves gear rack 4 along guides a-a which belong to slide 2. Gear rack 4 rotates gear 5. The coordinates of points E and D of gear 5 satisfy the equations: x_E=-e+r sin(β) and y_E=f(x)+v(x)-r cos(β); x_D=-e-r cos(β) and y_D=f(x)+v(x)+r sin(β). Points E and D describe curves on a fixed plane. The area of the curve described by point E is expressed by the integral l_E=∫(y_E)dx_E; [0,d]+∫(y_E)dx_E;[d,0]=r∫f(x)d[sin(n(2π/d)x)];[0,d]=ka_n. The area of the curve described by point D is expressed by the integral l_D=r∫f(x)d[cos(n(2π/d)x)]=kb_n; with limits [0,d], where r is the distance from the centre of gear 5 to points D and E.
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