Steven Boer

Design and Performance Optimization of Large Stroke Spatial Flexures

Flexure hinges inherently lose stiffness in supporting directions when deflected. In this paper a method is presented for optimizing the geometry of flexure hinges, which aims at maximizing supporting stiffnesses. In addition, the new ∞ -flexure hinge design is presented. The considered hinges are subjected to a load and deflected an angle of up to ±20 deg. The measure of performance is defined by the first unwanted natural frequency, which is closely related to the supporting stiffnesses. During the optimization, constraints are applied to the actuation moment and the maximum occurring stress. Evaluations of a curved hinge flexure, cross revolute hinge, butterfly flexure hinge, two cross flexure hinge types, and the new ∞ -flexure hinge are presented. Each of these hinge types is described by a parameterized geometric model. A flexible multibody modeling approach is used for efficient modeling while it accounts for the nonlinear geometric behavior of the stiffnesses. The numerical efficiency of this model is very beneficial for the design optimization. The obtained optimal hinge designs are validated with a finite element model and show good agreement. The optimizations show that a significant increase in supporting stiffness, with respect to the conventional cross flexure hinge, can be achieved with the ∞ -flexure hinge

A 2-DOF Large Stroke Flexure Based Positioning Mechanism

Flexure based stages are particularly important for vacuum applications because they combine low hysteresis, no wear and no contamination with a high supporting stiffness. However, flexure hinges inherently lose stiffness in supporting directions when deflected. Therefore the workspace to footprint ratio is limited. In this article we present the design and modeling of a two degrees of freedom cross flexure based stage that combines a large workspace to footprint ratio with high vibration mode frequencies. Because the mechanism is an assembly of optimized components, the stage is designed according to the exact constraint principle to avoid build-up of internal stresses due to misalignment. FEM results have been validated by measurements on an experimental test setup. The test setup has a workspace-area to footprint ratio of 1/32. The lowest measured natural frequency with locked actuators over a 60 × 60mm workspace was 80Hz.Copyright

Exact Constraint Design of a Two-Degree of Freedom Flexure-Based Mechanism

We present the exact constraint design of a two degrees of freedom cross-flexure-based stage that combines a large workspace to footprint ratio with high vibration mode frequencies. To maximize unwanted vibration mode frequencies the mechanism is an assembly of optimized parts. To ensure a deterministic behavior the assembled mechanism is made exactly constrained. We analyze the kinematics of the mechanism using three methods; Grublers criterion, opening the kinematic loops, and with a multibody singular value decomposition method. Nine release-flexures are implemented to obtain an exact constraint design. Measurements of the actuation force and natural frequency show no bifurcation, and load stiffening is minimized, even though there are various errors causing nonlinearity. Misalignment of the exact constraint designs does not lead to large stress, it does however decrease the support stiffness significantly. We conclude that designing an assembled mechanism in an exactly constrained manner leads to predictable stiffnesses and modal frequencies

Large Stroke Performance Optimization of Spatial Flexure Hinges

Flexure hinges inherently lose stiffness in supporting directions when deflected. In this paper a method is presented for optimizing the geometry of flexure hinges, while supporting stiffnesses are retained. These hinges are subjected to a load and deflected an angle of up to ±20°. The measure of performance is defined by the first unwanted eigenfrequency, which is closely related to the supporting stiffnesses. During the optimization, constraints are applied to the actuation moment and the maximum occurring stress. Evaluations of three cross flexure hinge types and a butterfly flexure hinge are presented. A flexible multibody modeling approach is used for efficient modeling. Each of these hinge types is described by a parameterized geometric model. The obtained optimal hinge designs are validated with a finite element model and show good agreement. The optimal solution of the butterfly flexure hinge shows the least decrease in the supporting stiffnesses of the evaluated hinges.

Analyzing overconstrained design of compliant mechanisms

Whereas the use of compliant mechanisms is favorable for high precision applications, the constraints must be dealt with carefully. In an overconstrained design the actual natural frequencies and stiffnesses can differ considerably from their intended values. For this reason the awareness and possibly the avoidance of an overconstrained condition is important. We have developed a kinematic analysis with which underconstraints and overconstraints can be detected. A finite element based multibody approach is applied which offers a flexible beam element that is particularly suited to model the wire and sheet flexures frequently encountered in compliant mechanisms. For each element a fixed number of independent discrete deformations are defined that are invariant under arbitrary rigid body motions of the element. In the kinematic analysis only deformations associated with low stiffnesses are allowed, whereas the remaining deformations are prescribed zero. A singular value decomposition is used to determine the rank of the Jacobian matrix associated with the dependent nodal coordinates. Column and row rank deficiency indicate an underconstrained and overconstrained system, respectively. For an overconstrained system a statically indeterminate stress distribution ca n be derived from the left singular matrix. In this way the overconstraints can be visualized clearly as is illustrated with examples of compliant straight guidance mechanisms. The possible solutions to eliminate the overconstraints are found easily from the visualization.