Ball and Burmester points in spherical kinematics and their special cases

On instantaneous invariants of hyperbolic planes

“…According to Özçelik andŞaka [9,10], the common points of the hyperbolic circling-point curve and the curve of thrice stationary curvature are called sixth-order Burmester points, see Figure 8. In order to find hyperbolic sixth-order Burmester points, by applying x = ty, t = 0 a seventh-degree equation depending on t is obtained as follows Similarly, the real roots of this last equation give the number of hyperbolic sixth-order Burmester points.…”

“…By using the circling-point curve and the cubic of twice stationary curvature curve based on instantaneous invariants in planar mechanisms, the parametric formulation of the Ball and Burmester points, cubic of thrice stationary curvature curve, and afterwards the fifth-order Burmester points were studied in Ting and Wang [8]. The existence conditions and the special cases of Ball and Burmester points in spherical kinematics were investigated and a parametric formulation with respect to the instantaneous invariants was determined by Özçelik andŞaka [9,10].…”