Influence analysis of the actuator displacements on stresses

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For the kinematics of the tripod manipulator, it is crucial to know how the constellation of actuators, based on their actual displacement, can affect the resulting position of the carried optical point in all six degrees of freedom ‐ all displacements and all rotations.

Moreover, the manipulator itself has to withstand all forces and stress resulting from the displacement of actuators. The tripod is also stabilized with three springs, each of them loaded with the prestress. Positions of these springs also may be changed during the design of the manipulator.

In total, there were 12 input parameters of the task, which is a massive extension to a previous study with only actuator displacements considered. For these three input parameters, a full-factorial scheme was used, leading to 27 computations in MSC.Nastran. However, this approach covered only the corners of the design space with a fixed interpolant level. Now, only 155 evaluations were needed for the expanded set of inputs and the creation of mathematical models for all ten outputs.


In the beginning, we coupled the UptimAI tool with the simulation software MSC.Nastran, with no need to interfere with its code or features. Then, the UptimAI tool began to set combinations of inputs for the Nastran. It used the UptimAI algorithm to process simulation results into the metamodel of forces and displacements of the tripod manipulator.

Features of the mathematical model could be easily shown on the example of one of the outputs, the von Mises stress. UptimAI sensitivity analysis identified input parameters with the significant ability to change the output. Unlike most of the other outputs, the stress is dependent almost entirely on displacements of actuators. The effect of springs and their positions is too low to be measurable.

From the UptimAI histogram, the overall information about the range of this output was shown as well as the shape of the probability density function.  Besides, it was possible to visualize the effect of each variable to the statistical properties of the model. Here the stress is ranging from 110 to 380MPa. From the influence analysis, it is apparent that setting the displacement of actuator 402 cannot lower the minimum value of stress below 110MPa. However, the probable maximum can be reduced by almost 30%.

Details responses of the von Mises stress level to changes in input parameters were apparent from UptimAI increment plots. Depicted dependencies of the output on particular inputs are separate from their mutual interactions. The UptimAI algorithm was able to catch the discontinuity in behavior based on the actuator displacements. That increased significantly the precision of the mathematical model over the commonly used interpolation with the quadratic polynomials. The model itself then consists of the summation of its all available increments.

The statistical nature of the model and the performed analysis was also used for the definition of design recommendation. The UptimAI preliminary optimization tool was used to identify ranges of input parameters resulting in decreased stress values in the tripod. The result suggesting the lowest actuator displacement possible was not a big surprise. Nevertheless, it was the explicit mathematical confirmation of conclusions based on general engineering intuition.


  • Deeper insight into the statistical effects on tripod’s behavior.
  • Fast design exploration. Set of only 155 FEM computations was sufficient to describe the problem with 12 input parameters and 10 outputs.
  • Simplified design task. The number of input parameters can be reduced while keeping the precision of the model.