The mechanical generation of planar curves by means of point trajectories, line and circle envelopes: A unified treatment of the classic and generalized Burmester problem

It is herein addressed the generation of planar curves by means of circles envelopes. The theoretical approach follows from a combined use of intrinsic geometry and the derivatives of Euler-Savary equation for conjugate profiles. The analytical results deduced are general and include, as particular cases, the formulas for the computation of classic and generalized Burmester points. Furthermore, also as particular case, follows the generation of planar curves as envelopes of a moving straight line. A new analytical form of the cubic of stationary is also presented. All the results are expressed in terms of classic kinematic invariants. In the Appendix the relationships of these invariants with those named after Bottema are deduced. Numerical examples are also discussed. (C) 2019 Published by Elsevier Ltd.