Computer Aided Geometric Design of Motion InterpolatesThis paper studies continuous computational geometry of motion and develops a method for Computer Aided Geometric Design (CAGD) of motion interpolants. The approach uses a mapping of spatial kinematics to convert the problem of interpolating displacements to that of interpolating points in the space of the mapping. To facilitate the point interpolation, the previously unorientable mapping space is made orientable. Methods are then developed for designing spline curves in the mapping space with tangent, curvature and torsion continuities. The results have application in computer animation of three-dimensional objects used in computer graphics, computer vision and simulation of mechanical systems. 756 / Vol. 116, SEPTEMBER 1994 Transactions of the ASMS Copyright © 1994 by ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/25/2015 Terms of Use: http://asme.org/terms

With the introduction of generalized function sets (GF set) to represent the characteristics of the end-effectors of parallel mechanisms, two classes of GF sets are proposed. The type synthesis of parallel mechanisms having the second class GF sets and two dimensional rotations, including 2-, 3-, and 4DOF parallel mechanisms, is investigated. First, the intersection algorithms for the GF sets are established via the axiom of two dimensional rotations. Second, the kinematic limbs with specific characteristics are designed according to the axis movement theorem. Finally, several parallel mechanisms having the second class GF sets and two dimensional rotations have been illustrated to show the effectiveness of the proposed methodology.

What most distinguished parents who refused from those who accepted randomization was not their knowledge and information about randomized clinical trials. By far, the majority of QIs that accurately predicted acceptors and refusers involved parents' beliefs, values, and perceptions. Further research is needed to determine interventions that may enable the healthcare team to provide information and decisional support most effectively to improve the informed consent process.

This paper deals with discrete computational geometry of motion. It combines concepts from the fields of kinematics and computer aided geometric design and develops a computational geometric framework for geometric construction of motions useful in mechanical systems animation, robot trajectory planning and key framing in computer graphics. In particular, screw motion interpolants are used in conjunction with deCasteljau-type methods to construct Bezier motions. The properties of the resulting Bezier motions are studied and it is shown that the Bezier motions obtained by application of the deCasteljau construction are not, in general, of polynomial type and do not possess the useful subdivision property of Bernstein-Bezier curves. An alternative form of deCasteljau algorithm is presented that results in Bezier motions with subdivision property and Bernstein basis function. The results are illustrated by examples.

We prospectively assessed the pharmacokinetics of methotrexate, mercaptopurine, and erythrocyte thioguanine nucleotide levels in a homogenous population of children with lower risk acute lymphoblastic leukemia and correlated pharmacokinetic parameters with disease outcome. The maintenance therapy regimen included daily oral mercaptopurine (75 mg/m2) and weekly oral methotrexate (20 mg/m2). One hundred ninety-one methotrexate doses and 190 mercaptopurine doses were monitored in 89 patients. Plasma drug concentrations of both agents were highly variable. The area under the plasma concentration-time curve (AUC) of methotrexate ranged from 0.63 to 12 μmol•h/L, and the AUC of mercaptopurine ranged from 0.11 to 8 μmol•h/L. Drug dose, patient age, and duration of therapy did not account for the variability. Methotrexate AUC was significantly higher in girls than boys (P = .007). There was considerable intrapatient variability for both agents. Erythrocyte thioguanine nucleotide levels were also highly variable (range, 0 to 10 pmol/g Hgb) and did not correlate with mercaptopurine dose or AUC. A Cox regression analysis showed that mercaptopurine AUC was a marginally significant (P = .043) predictor of outcome, but a direct comparison of mercaptopurine AUC in the remission and relapsed patient groups failed to show a significant difference. Methotrexate and mercaptopurine plasma concentrations and erythrocyte thioguanine nucleotide levels were highly variable, but measurement of these pharmacokinetic parameters at the start of maintenance will not distinguish patients who are more likely to relapse.

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In this paper, we explore the notion of kinematic convexity for rigid body displacements. Previously, we have shown that when spatial rigid body displacements are represented by dual quaternions, an oriented projective space is better suited for the image space of displacements. Geometric algorithms for rigid body motions become more general and elegant when developed from the perspective of oriented projective geometry. By extending the concept of convexity in affine geometry to oriented projective geometry of the image space of rigid body displacements, we define the concept of kinematic convexity. This concept, apart from being theoretically significant, facilitates localization of a displacements and provides a measure of the kinematic separation useful in collision prediction, interference checking, and geometric analysis of swept volumes.

SUMMARYA method is presented for the type synthesis of a class of parallel mechanisms having one-dimensional (1D) rotation based on the theory of Generalized Function sets (GF sets for short), which contain two classes. The type synthesis of parallel mechanisms having the first class GF sets and 1D rotation is investigated. The Law of one-dimensional rotation is given, which lays the theoretical foundation for the intersection operations of GF sets. Then the kinematic limbs with specific characteristics are designed according to the 2D and 3D axis movement theorems. Finally, several synthesized parallel mechanisms have been sketched to show the effectiveness of the proposed methodology.