Fillets are commonly used in mechanical engineering in order to avoid singularities and then stress concentrations.
The goal is here to “put down in writing” methods I’ve been using to analytically calculate fillets; these are one solution among others (and not necessary the best ones or the simplest ones), but I’m good with them and they answer to my needs (if some of you want to share other methods, I’ll be pleased to devote a specific section and the author will be cited).
There are different types of fillets; the simplest of them is the arc of a circle that answers to a practical need, the use of a ball-nose cutter. In the meantime I’ve discovered other methods for curves transition, notably used by topographers in the design of road networks or railway ones for example (it uses clothoids or Cornu’s spirals – the later ones are also called Euler’s spirals especially in the English speaking world).
1- Fillets using an arc of a circle
1-1 The basis
The figure here after presents a fillet in arc of a circle.
It be characterized by 2 straight lines and , by its radius , by its centre and by the points of tangency et we have to calculate.