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A French curve is a template usually made from metal, wood or plastic composed of many different curved segments. It is used in manual drafting and in fashion design to draw smooth curves of varying radii. The curve is placed on the drawing material, and a pencil, knife or other
Ludwig Burmester. Ludwig Ernst Hans Burmester (5 May 1840 – 20 April 1927) was a German kinematician and geometer.. His doctoral thesis Über die Elemente einer Theorie der Isophoten (from German: About the elements of a theory of isophotes) concerned lines on a surface defined by light direction.
French curves are used for drawing curves which cannot be drawn with compasses. A faint freehand curve is first drawn through the known points; the longest possible curve that coincides exactly with the freehand curve is then found out from the French curves. Finally, a neat continuous curve is drawn with the aid of the French curves.
The drafter uses several technical drawing tools to draw curves and circles. Primary among these are the compasses, used for drawing arcs and circles, and the French curve, for drawing curves. A spline is a rubber coated articulated metal that can be manually bent to most curves.
An equation was given for various drafting tools, such as the triangle being x=ay, the compass being X²+y²=r² and a longer equation for french curves. I would be very interested to learn about how these equations function with the traditional real-world french curve template for example. Lots to be said about french curves!
A space curve; the vectors T, N, B; and the osculating plane spanned by T and N. In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.
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Burmester's approach to the synthesis of a four-bar linkage can be formulated mathematically by introducing coordinate transformations [T i] = [A i, d i], i = 1, ..., 5, where [A] is a 2×2 rotation matrix and d is a 2×1 translation vector, that define task positions of a moving frame M specified by the designer.