This paper presents a new velocity blending approach to the problem of task space trajectory generation. To compare this technique with others, a generalized formulation for task space trajectory blending is also developed. It is shown that task space velocity blending provides a substantial simpli cation in both representation and computational complexity over previously proposed methods. While some residual orientation error is incurred by mathematical approximations, it is analytically shown that this error is small and a correction method is provided. Finally, examples are given, our real-time implementation is described, and implementational considerations are addressed.