Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

This paper introduces a link-type tracked vehicle, which is developed for potential applications such as Ž re Ž ghting, handicapped assistance and mine detection in various hazardous environments. The vehicle consists of three parts — front frame, rear frame and body. The front frame is connected to the rear frame by a rotational passive adaptation mechanism, which is the driving mechanism of t...

Assumption: The body shape relative to the body frame is a given function of time B0(t). We call this the standard shape. The current body shape B(t) is obtained under a translation and rotation of the body frame. The latter is defined by a positional matrix. To say that locomotion has occurred at time t means we have realized at time t a nonzero translation. Example: steady locomotion in two d...

Consider a 3-dimensional rigid body, B. Let C denote the point in B which is fixed during subsequent spherical motions. Choose a fixed reference frame, F whose origin lies at point C. To understand what happens to a rigid body during a spherical motion, select an arbitrary point, P0, in B. Let ~v0 denote the vector from the origin of this fixed reference frame to P0. I.e., ~v0 denotes the coord...

Consider a 3-dimensional rigid body, B. Let C denote the point in B which is fixed during subsequent spherical motions. Choose a fixed reference frame, F whose origin lies at point C. To understand what happens to a rigid body during a spherical motion, select an arbitrary point, P0, in B. Let ~v0 denote the vector from the origin of this fixed reference frame to P0. I.e., ~v0 denotes the coord...