Tensegrity mechanisms using linear springs as tensioned elements constitute an interesting class of mechanisms. When considered as manipulators, their workspace remains however to be defined in a generic way. In this article, we introduce a workspace definition and at the same time a computation method, based on the estimation of the workspace boundaries. The method is implemented using a continuation method. As an example, the workspace assessment of a two degrees of freedom (DOF) planar tensegrity mechanism is presented.

One of the principal objectives of studying biogeochemical cycles is to obtain precise estimates of the main fluxes, such as total, new and export oceanic productions. Since models can incorporate the a priori knowledge of the most important processes, they are increasingly used for this purpose. However, biogeochemical models are characterized by a large number of poorly known parameters. Moreover, the available data are rather sparse in both time and space, and represent concentrations, not fluxes. Therefore, the major challenge is to constrain the relevant fluxes using information from a limited number of observations and from models incorporating poorly known internal parameters. The present study attempts to meet this challenge. In a 1D framework at the DYFAMED station (NW Mediterranean Sea), near-monthly nitrate and chlorophyll profiles and daily surface chlorophyll concentrations are assimilated in a coupled dynamical–biological model using the tangent linear and adjoint models. Following sensitivity analyses that show that some parameters cannot be recovered from the data set used, assimilation of observed 1997 data is performed. The first inversion considered clearly shows that, in agreement with previous studies, (1) the data impose a C/Chl ratio that varies with depth (i.e. light) and (2) the “initial” conditions (e.g. winter nitrate profile) strongly constrain the annual biogeochemical fluxes. After assimilation of the 1997 data, the agreement between the data and the model is quantitatively improved in 1995 and 1996, which can be considered a good validation of the methodology. However, the order of magnitude of the biogeochemical fluxes, and especially of the particulate export and regenerated production, are not correctly recovered. An analysis of the simulations shows that this result is associated with a strong decrease in zooplankton concentrations. An additional constraint of maintaining acceptable levels of zooplankton is therefore added. The results are improved, but remain unsatisfactory. A final inversion, which takes into account the a priori estimates of the major annual fluxes, is then performed. This shows that there is no inconsistency between the NO 3 and chlorophyll data, the order of magnitude of the fluxes and the model. The work therefore demonstrates that recovering biogeochemical fluxes from available data of concentrations and stocks is not a straightforward exercise: the coverage and type of observations, and the nonlinearities of the biogeochemical model all contribute to this difficulty.