The present paper proposes an instantaneous inverse kinematic solution for redundant manipulators based on virtual arms. The virtual arm has the same kinematic structure as the manipulator except that its end-point is located on the joint or link of the manipulator. When the appropriate virtual arms are used, the configuration of the manipulator can be represented by a set of end-points of the virtual arms. First of all, this paper formalizes the kinematics of virtual arms and derives instantaneous inverse kinematics. Then, the method is applied to winding control for hyper-redundant manipulators. The winding control presented here is divided into two steps: 1)planning desired positions for virtual end-points, 2)integrating them into the joint trajectory of the manipulator. The desired positions of each virtual arm can be computed in a parallel and distributed way and it is not necessary to consider joint space of the manipulator. Finally computer simulations show that the winding control for a hyper-redundant manipulator can be performed in 3D-space.