Modeling of Equivalent Stiffness of Adaptive Platforms with the Parallel Structure Executive Mechanism
Keywords:
Stewart Platform, Actuator, Equivalent Stiffness, Stiffness MatrixAbstract
Purpose: One of ways to increase accuracy and reliability of electromechanical systems with parallel structure such as an adaptive
platform (for example n-pods) is application of control loop dynamics models allowing to predict special positions (jamming) and to
calculate the optimal control laws. Stiffness characteristics of such systems are the key element of predictive models. Therefore, the
purpose of this research is to develop methods of constructing a matrix of equivalent stiffness of an adaptive platform moved by packets
of actuators taking into account changes of the action line of the actuators. Results: There have been obtained simple formulae for
calculating the matrix of equivalent stiffness of an adaptive platform moved by packets of an arbitrary number of actuators. It has
been shown that in contrast to the formula for a packet of springs the formula for adaptive platforms should be modified to take into
account changes of length and the action line of the actuators. The given numerical example for Stewart platform (hexapod) confirms
significant effect of these factors. It has been proven that in case of small angular displacements of a platform the proposed formula
after simplification is analogous to the formula for calculating equivalent stiffness of matrix package springs. There has been obtained
a formula for calculating a symmetric stiffness matrix of the actuator. Practical relevance: The proposed simple algorithms for
calculating matrix equivalent stiffness of an adaptive platform are effective for implementing the predictive model allowing to predict
occurrence of specific positions and to develop algorithms for their prevention in real time that will increase reliability of the system
and its capacity.