evolution of space curves using type-3 bishop frame

In this paper, firstly, we introduce a new version of bishop frame using a common vector field as normal vector field of a regular curve and call this frame as type-3 bishop frame. geometric visualization for both frenet frame and type-3 bishop frame are plotted. secondly, time evolution equation for type-3 bishop frame and type three bishop curvatures are obtained and we plotted the evolving curve via the numerical integration of type-3 bishop serret frenet equations. finally, surfaces generated by evolving a regular space curve in r3 as it evolves over time with arbitrary velocities attached to type-3 bishop frame are obtained. we plotted these surfaces via numerical integration of gauss-weingarten equations.