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.

This study presents a new kinetostatic model for humanoid robots (HRs). Screw theory, together with Assur virtual chains and Davies' method, provides the required tools for the proposal of both the kinematic and static parts of the kinetostatic model. Our kinetostatic model is able to estimate the forces and couples generated at the axes of each joint of the robot, as well as one unknown contact condition between the robot and the environment around it. The proposed model is also very versatile and free of fixed coordinates and, therefore, it allows for an estimate of a great amount of information on the HR. Some results, obtained from computer simulation, are presented to validate the versatility of the proposed technique.

In this paper, a new method – named lumped kinetostatic modeling – to analyze the effect of the link flexibility on the mechanism's stiffness is provided. A new type of mechanism whose degree of freedom (dof) is dependent on a passive constraining leg connecting the base and the platform is introduced and analyzed. With the proposed kinetostatic model, a significant effect of the link flexibility on the mechanism's precision has been demonstrated. The influence of the change in structure parameters, including material properties, on the system behavior is discussed. In the paper, the geometric model of this kind of mechanism is first introduced. Then, a lumped kinetostatic model is proposed in order to account for joint and link compliances; some results and design guidelines are obtained. Finally, the optimization of the precision is addressed using a genetic algorithm.