Design And Application Of Transition Curve

The theme of this thesis is several kinds of designing and applications about transition curves, mainly related to the construction of the transition curves, the study of curvature monotony, the continuity at endpoints and some practical applications. Since transition curves have been widely used in fields of CAD, numerical control machining, road design and robot trajectories et al, the research of them is very important.In chapter1, the research background is given. In chapter 2, six quasi-cubic Bézier curves with only three control points are constructed by means of a study on base functions, and the sufficient conditions of monotone curvature are given. Also, we proposed two types of new ?- curves with a shape parameter in chapter 3, which only have three control points. One adopts sin t, t and 1 as its basis while another adopts cos t, t and 1, also the sufficient conditions for monotone curvature of these ?- curves are deduced. Then, in chapter 4, a new kind of minimal degree polynomial potential function which can make transition curve reaching Ck continuity at endpoints and another new kind of mixed trigonometric potential function with a shape parameter which can reach high coincidence at one side of transited curves on conditions of keeping 1C continuity at endpoints are constructed. The reasons for inflection point in cylinder profile of rotary vane compressor are analyzed in chapter 5, and a new design idea about the profile is presented. The cubic Bézier profile is designed for the purpose of low intake volume but high internal volume ratio, and is suitable for the compressor of high internal pressure ratio but low discharge volume. On the contrary, the quasi-quartic Bézier profile is adopted to achieve high intake volume but low internal volume ratio, and is suitable for the compressor of low internal pressure ratio but high discharge volume. Finally, conclusions and further research about this paper are given.