Abstract: A construction is presented, which is comprised of two piezoelectric bending cantilevers, of different lengths, called a first bender and a second bender respectively, in which both benders bend in opposite directions. The second bender is mechanically in series connected to the first bender, thereby increasing the rotation angle of the tip of the second bender. The length of the second bender is chosen thus that in sinusoidal excitation, the tip of the second bender remains at the same point throughout the entire cycle, while it does undergo rotation. In this fashion a virtual axis at the tip of the second bender is created. The width of both benders is chosen such that the moment that the second bender can exert on an object that is connected to it, enables the construction to drive an optical element to scanning vibratory rotary motion with a large angle at high frequencies.

Abstract: A construction of benders is disclosed in which benders of single and double lengths are conjoined in a particular manner, which results in constructions in which objects can be rotated but not translated. Three constructions are detailed, one in which an object is rotated over two unit angles alpha, whereas a second construction is disclosed whereby an object is rotated over four unit angles alpha, while a third construction is disclosed in which an object is rotated over eight unit angles alpha. An example is disclosed in which the repeated application of identical units will result in larger rotation angles, still without causing translation.

Abstract: A construction of benders is disclosed in which benders of single and double lengths are conjoined in a particular manner, which results in constructions in which objects can be rotated but not translated. Three constructions are detailed, one in which an object is rotated over two unit angles alpha, whereas a second construction is disclosed whereby an object is rotated over four unit angles alpha, while a third construction is disclosed in which an object is rotated over eight unit angles alpha. An example is disclosed in which the repeated application of identical units will result in larger rotation angles, still without causing translation.

Abstract: A process for the treatment of aromatic polyamide fibers, which are suitable for use in construction materials and rubbers, as well as so treated fibers and shaped articles strengthened with these fibers.