Complications in and post conventional invasive procedures makes minimal invasive surgery well accepted in society. It causes less pain and scarring, faster recovery, and reduces operative trauma for patients. To overcome the difficulties of limited steerability and stiffness control of conventional scope, a continuously curving manipulator actuated by smart material named shape memory alloys (SMA) is proposed in this paper. The segmented scope consisted of a compression spring backbone and three SMA actuators to dynamically control the shape of each segment of the manipulator as and when required. A detailed study was carried out to simulate the constraints of the manipulator and fit it to a given random curve in a 3-dimensional (3D) space in the best possible way. The paper also includes testing of one segment of the prototype with bending angles and force produced during actuation. Actuation time and cooling time, which is issue using SMA practically, are also discussed briefly. The manipulator seems to be a promising device to be able to follow given random complex 3D trajectories and vary segment stiffness as and when required.