In this paper, we describe how manipulator arms with end-effectors and payloads, if any, can be modeled using superellipsoids. Superellipsoids are very flexible convex solids. They are easy to manipulate by mathematical transformations and also possess a well defined inside-outside function, which to a great extent facilitates simulation of object interactions. A systematic way of determining transformation matrices between manipulator links, which are described as superquadric links, is presented. We also present how object detection and collision avoidance can be achieved. This technique has been implemented in a hybrid telerobotic simulator for undersea operations. It has also proved to be efficient for simulation of pick-and-place operations.