Dear folks,
there is still an open problem nowadays which needs and answer at the true beginning of things, i-e mechanical design. The open problem is the one of achieving very hish speed machine-tools.
Firstly, lets define what we mean about very high speed. In fact, this means higher accelerations so that the time spent moving from one machining trajectory to the next is minimized, thereby requiring faster accelerations.
Most machine tools have Cartesian based mechanisms being of serial topology making them very flexible. Recebt trends led the application of the hexapods (Gough platform) in that sense but were still plagued by limited capacity to achieve machining operations. At the moment, only roughing can be done at very limited accelerations.
The problem comes from improper linear actuators.
A new generation of these linear actuators making use of parallel mechanisms such as four-bars can solve this issue and I have done the kinematics analysis of those devices in my latest book chapter:
L. Rolland. Kinematics Synthesis Of A New Generation Of Rapid Linear Actuators For High Velocity Robotics With Improved Performance Based On Parallel Architecture, book chapter, Advanced Strategies for Robot Manipulators, Ehsan Shafiei Editor, Sciyo Publishers International, Lubjana, 2010.
Luc