Tendon-based parallel manipulators with n d.o.f. use at least m = n + 1 tendons to guide the endeffector along a given trajectory. Since tendons can only transmit limited and tractive forces, it is essential to apply a valid tendon force distribution. Due to safety and precision requirements, a combined position and force control is needed where the force calculation delivers the desired tendon force distributions. The high dynamic potential of the robot demands for realtime capable algorithms. To avoid steps in the motor torques the calculated tension force distributions also have to be continuous along the trajectory. In this paper, a new algorithm for tendon force distribution calculations capable for usage on a realtime system is proposed and its continuity is proven.

This paper presents an algorithm to determine feasible force distributions for parallel wire robots in closed-form. The force distributions are continuous along trajectories and differentiable at most of the points. The computational efforts are strictly bounded and small even for large numbers of wires. The algorithm is compared to other approaches for calculation of force distribution in terms of the numerical effort and their applicability for control purposes.

OpenModelica is a unique large-scale integrated open-source Modelica-and FMI-based modeling, simulation, optimization, model-based analysis and development environment. Moreover, the OpenModelica environment provides a number of facilities such as debugging; optimization; visualization and 3D animation; web-based model editing and simulation; scripting from Modelica, Python, Julia, and Matlab; efficient simulation and co-simulation of FMI-based models; compilation for embedded systems; Modelica-UML integration; requirement verification; and generation of parallel code for multi-core architectures. The environment is based on the equation-based object-oriented Modelica language and currently uses the MetaModelica extended version of Modelica for its model compiler implementation. This overview paper gives an up-to-date description of the capabilities of the system, short overviews of used open source symbolic and numeric algorithms with pointers to published literature, tool integration aspects, some lessons learned, and the main vision behind its development.

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Completely and redundantly restraint tendon-based Stewart platforms demand for an appropriate distribution of tendon forces to control the platform on a given trajectory. Thus, position control has to be extended by a tendon force controller which generates continuous and feasible force values. The computation of such force distributions can be formulated as a constrained optimization problem. Solving the problem is numerically expensive and requires an algorithm which is capable to be integrated into a realtime environment. In this paper, a new algorithm for tendon force distribution calculations capable for usage on a realtime system is proposed.