Efficient dynamic simulation of flexible link manipulators with PID control

For accurate simulations of the dynamic behavior of flexible manipulators the combination of a perturbation method and modal analysis is proposed. First, the vibrational motion is modeled as a first-order perturbation of a nominal rigid link motion. The vibrational motion is then described by a set of linear timevarying equations. Next, the number of degrees of freedom is reduced by applying a modal reduction technique. The proportional part of the control system is explicitly included in the modal analysis. The applicability of the method is demonstrated by simulating the controlled trajectory motion of a spatial flexible three-degree of freedom manipulator with PID control

Flexible multibody modelling for the mechatronic design of compliant mechanisms

In high precision equipment the use of compliant mechanisms is favourable as elastic joints offer the advantages of low friction and no backlash. To satisfy exact constraint design the mechanism should have exactly the required degrees of freedom and constraints so that the system is kinematically and statically determinate. For this purpose we propose the following kinematic analysis using a flexible multibody modelling approach. In compliant mechanisms the system’s degrees of freedom are presented clearly from the analysis of a system in which the compliant part are free to deform while the support is considered rigid. If the Jacobian matrix associated with the dependent coordinates is not full column or row rank, the system is underconstraint or overconstraint. The rank of this matrix is calculated from a singular value decomposition. For an underconstraint system any motion in the mechanism that is not accounted for by the current set of degrees of freedom is visualised using data from the left singular matrix. For an overconstraint system a statically indeterminate stress distribution is derived from the right singular matrix and is used to visualise the overconstraints. In the next step of the mechatronic design the system’s closed-loop stability and performance are considered. Valuable insight is obtained from a dynamic analysis in which the non-linear models are linearised in selected configurations to derive natural frequencies and mode shapes

Flexible multibody modelling for exact constraint design of compliant mechanisms

In high precision equipment, the use of compliant mechanisms is favourable as elastic joints offer the advantages of low friction and no backlash. If the constraints in a compliant mechanism are not carefully dealt with, even small misalignments can lead to changes in natural frequencies and stiffnesses. Such unwanted behaviour can be avoided by applying exact constraint design, which implies that the mechanism should have exactly the required degrees of freedom and non-redundant constraints so that the system is kinematically and statically determinate. For this purpose, we propose a kinematic analysis using a finite element based multibody modelling approach. In compliant mechanisms, the system’s degrees of freedom are presented clearly from the analysis of a system in which the deformation modes with a low stiffness are free to deform while the deformation modes with a high stiffness are considered rigid. If the Jacobian matrix associated with the dependent coordinates is not full column or row rank, the system is under-constrained or over-constrained. The rank of this matrix is calculated from a singular value decomposition. For an under-constrained system, any motion in the mechanism that is not accounted for by the current set of degrees of freedom is visualised using data from the right singular matrix. For an over-constrained system, a statically indeterminate stress distribution is derived from the left singular matrix and is used to visualise the over-constraints. The analysis is exemplified for the design of a straight guiding mechanism, where under-constrained and over-constrained conditions are visualised clearly