A new method to fit specific types of conics to scattered data points is introduced. Direct, specific fitting of ellipses and hyperbolæ is achieved by imposing a quadratic constraint on the conic coefficients, whereby an improved partitioning of the design matrix is devised so as to improve computational efficiency and numerical stability by eliminating redundant aspects of the fitting procedure. Fitting of parabolas is achieved by determining an orthogonal basis vector set in the Grassmannian space of quadratic conic forms. The linear combination of the basis vectors which fulfills the parabolic condition and has a minimum residual is determined using Lagrange multipliers. 1

With regard to planar parallel manipulators, a general classification of singularities into three groups is introduced. The classification scheme relies on the properties of the Jacobian matrices of the manipulator at hand. The Jacobian matrices of a general class of planar parallel manipulators are derived and the three types of singularities are identified for them. This class contains 20 manipulators constructed with three different combinations of legs of the PRR, PPR, RRR and RPR types, P and R representing prismatic and revolute pairs, respectively.

For original article see ibid., vol.C-31, no.10, p.853-61, Oct. 1986. Although the P-functions of the original paper are an aesthetically pleasing method for optimizing binary decision programs, existing procedures are probably more efficient. Current research applying Prolog to the automatic design of microprograms is outlined.>

A spline-based method of programming smooth trajectories for pick-and-place operations is introduced. Unlike continuous-path operations, which impose a unique Cartesian trajectory, an infinite number of smooth trajectories can be described between any given pick and its corresponding place configuration. The method begins with the mapping of the pick and the place configuration in Cartesian space into joint-coordinate space, using a general-purpose inverse kinematics package that handles singularities and redundancies. Next, a trajectory, composed of a C/sup 2/-continuous, periodic cubic spline segment, is defined between the pick and the place configurations in the joint-coordinate space. It is demonstrated that C/sup 2/-continuity will prevail in Cartesian space as well. The software implementing this method includes a graphics package as well as an interface to an offline programming system to realize the synthesis of the actual robot motion. Details of the procedure are illustrated with a numerical example applied to a commercial industrial robot.>