Abstract: A golf putter useful for training a golfer in improving putting skills includes a club head which is dimensioned in a lateral direction to the club shaft and balanced with the shaft so as to permit the head to lie flat upon a playing surface with the club shaft standing upright while unattended. Alignment marks or a detachable alignment guide permit the golfer to observe the alignment of the club face or a hole with respect to a golf ball, while the club is unattended with the shaft inclined at a substantial angle from the vertical.

Abstract: A method for constructing the Minkowski sum and derivative morphological combinations of arbitray polyhedra uses operations supported in current CAD/CAM systems. The method has application to three-dimensional modeling of very large scale integrated (VLSI) circuits, their design and simulation of fabrication, and to automated mechanical assembly. The method also has application to n-dimensional modeling in robotics as well as other applications of CAD/CAM systems. In one aspect, an exact Minkowski sum of two polyhedra is obtained by a generalization of sweeping a face along an edge. More generally, according to a second aspect, the Minkowski sum of two polyhedra is computed as the union of linear translational sweeps enabled by the first aspect. The method implements techniques and formulas which greatly reduces the overall cost of the computation of Minkowski sums and, in particular, avoids computations involving non-transversal polyhedra.

Abstract: A golf putter useful for training a golfer in improving putting skills includes a club head which is dimensioned lateral direction to the club shaft and balanced with the shaft so as to permit the head to lie flat upon a playing surface with the club shaft standing upright while unattended. Alignment marks or a detachable alignment guide permit the golfer to observe the alignment of the club face or a hole with respect to a golf ball, while the club is unattended. The detachable alignment guide may be an elongated tubular element having a longitudinal slit at one end thereof for fitting onto an upstanding riser on the top surface of the club head. The guide extends from the riser, vertically above the club head striking face, and over the golf striking face, and over the golf ball being putted.

Abstract: Cumulative translational sweeps are used to shape geometric objects in a computer model, and they permit display of the resulting changes in shape in the object modelled, and control of processes involving the object modelled. If the geometric object is polyhedral, the cumulative translational sweeps, by creating additional facets, effect selective rounding along model edges and around model vertices. This permits computer modelling of the growth of layers, encompassing in addition to flat surface growth, growth with rounding around corners and over obstacles. Such growth occurs in the manufacture of semiconductors. Modelling a change in a solid structure in stages of growth (or shrinking) and of rounding, as might take place during processing of integrated circuits is achieved by controlled sweep sequences that sweep the structure a finite number of times in accordance with a rayset and stipulated parameters of shape, balance, convexity/concavity, degree of faceting, and memory limitation.

Abstract: A method and apparatus for calibrating a robot and using the results of this calibration to compensate for inaccuracies of the robot and also to diagnose robot deterioration. The method includes moving the robot to a set of nominal positions, commanded by the robot controller or measured by position encoders built into the robot, and determining the associated actual positions by measuring the robot position with an independent accurate measuring means or by aligning the robot end effector with an accurate calibration mask. The calibration results are stored and subsequently used to compensate for robot inaccuracy so that the robot moves to the actual desired positions.

Abstract: An exercising device has a body made from one solid continuous piece of contoured rod using the variable friction resistance rope principle. The body is formed having two spaced rod sections, one end of each of the rod sections bends inwardly and extends towards a center line with the two rod sections then bending to extend substantially parallel to a point where they then bend towards each other and join to form a curved end; this arrangement forms a neck and shoulder portion. The two spaced rod sections taper towards each other where they form short parallel rod sections at the opposite end of the body with the ends of the rods joining to form a second curved end. Resistance is varied by passing the rope around the rod a selected number of turns. The number of loops around the rod directly affect the friction resistance developed.

Abstract: A tubular device for holding balls and dispensing them. The device is shaped spherically at the bottom and supports the balls therein and is formed of elastic or resilient material, a slot at the bottom can be opened by temporarily deforming the device by hand, this will release one or more balls.