Tensegrity mechanisms are composed of rigid and tensile parts that are in equilibrium. They are interesting alternative designs for some applications, such as modeling musculo-skeleton systems. Tensegrity mechanisms are more difficult to analyze than classical mechanisms as the static equilibrium conditions that must be satisfied generally result in complex equations. A class of planar one-degree-of-freedom tensegrity mechanisms with three linear springs is analyzed in detail for the sake of systematic solution classifications. The kinetostatic equations are derived and solved under several loading and geometric conditions. It is shown that these mechanisms exhibit up to six equilibrium configurations, of which one or two are stable, depending on the geometric and loading conditions. Discriminant varieties and cylindrical algebraic decomposition combined with Groebner base elimination are used to classify solutions as a function of the geometric, loading, and actuator input parameters.

Few existing Computer Aided Design (CAD) systems provide assistance to designers in developing geometric concepts at the early design stages. Instead they require a high level of precision and detail suited to detail design. To support the early geometric design, a CAD system should provide utilities for the rapid capture and iterative development of vague geometric models. This paper presents a pilot system that is being developed based on such a vision. The system has adopted minimum commitment modelling and incremental refinement as the guiding principles. The representation of geometric configuration is based on a parametric and constraint-based geometric design model, and provides a uniform representation of the approximate and precise size and location parameters. A constraint-based mechanism has been developed for processing geometric information. The use of the system in assisting the development of a geometric configuration is also demonstrated. Finally, features and limitations of the system as well as relations to relevant works are discussed, and based on this a number of key research directions are established.

Along with the classical requirements on B-splines bases(minimal support, positivity, normalization)we show that it is natural to introduce an additional“end point property". When dealing with multiple knots,this additional property is exactly the appropriate requirementto obtain the poles of nondegenerate splinesas intersections of osculating flats at consecutive knots.