Experimental Characterization of a Large-Range Parallel Kinematic XYZ Flexure Mechanism

Previously, we reported the conceptual design of a novel parallel-kinematic flexure mechanism that provides large and decoupled motions in the X, Y, and Z directions, along with good actuator isolation, and small parasitic error motions (Awtar, S., Ustick, J., and Sen, S., 2012, “An XYZ Parallel-Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom,” ASME J. Mech. Rob., 5(1), p. 015001). This paper presents the detailed design and fabrication of a high-precision experimental setup to characterize and validate the motion attributes of this proposed flexure design via comprehensive measurements. The unique aspects of this experimental setup include a novel modular construction and exact-constraint assembly of the flexure mechanism from 12 identical parallelogram flexure modules. The flexure mechanism along with the sensing and actuation setup in the experiment is designed to enable large range (10 mm) in each direction. Experimental measurements and finite-elements analysis demonstrate <3% variation in motion direction stiffness, 20.4% lost motion, <11.6% cross-axis error, <3.3% actuator isolation, and <9.5 mrad motion stage rotation over the entire 10 mm × 10 mm × 10 mm range of motion.

Iterative method to the coupled operator matrix equations with sub-matrix constraint and its application in control

A finite iterative algorithm is presented for solving the numerical solutions to the coupled operator matrix equations in Zhang (2017b). In this paper, a new finite iterative algorithm is presented for solving the constraint solutions to the coupled operator matrix equations [Formula: see text], where the constraint solutions include symmetric solutions, bisymmetric solutions and reflexive solutions as special cases. If this system is consistent, for any initial constraint matrices, the exact constraint solutions can be obtained by the introduced algorithm within finite iterative steps in the absence of the roundoff errors. Also, if this system is not consistent, the least-norm constraint solutions can be obtained within the finite iteration steps in the absence of the roundoff errors. Furthermore, if a group of suitable matrices are given, the optimal approximation solutions can be derived. Finally, several numerical examples are given to show the effectiveness of the presented iterative algorithm.

Shifted axis angular positioning mechanisms – unconventional use of exact constraint design

Paper presents some remarks about designing angular positioners having significant angular displacement and shifted axis of rotation. Those driving mechanism are useful in specific applications where mechanism wraps around other object or there is a need of rotation around virtual axis. Examples of those applications like orthotic robots or gimbals for panoramic motions where developed at Faculty of Mechatronics WUT. Usage of exact constraint method was described including its influence to a kinematic structure of designed mechanism.

Modal Measurements and Model Corrections of A Large Stroke Compliant Mechanism

In modelling flexure based mechanisms, generally flexures are modelled perfectly aligned and nominal values are assumed for the dimensions. To test the validity of these assumptions for a two Degrees Of Freedom (DOF) large stroke compliant mechanism, eigenfrequency and mode shape measurements are compared to results obtained with a flexible multibody model. The mechanism consists of eleven cross flexures and seven interconnecting bodies. From the measurements 30% lower eigenfrequencies are observed than those obtained with the model. With a simplified model, it is demonstrated that these differences can be attributed to wrongly assumed leaf spring thickness and misalignment of the leaf springs in the cross flexures. These manufacturing tolerances thus significantly affect the behaviour of the two DOF mechanism, even though it was designed using the exact constraint design principle. This design principle avoids overconstraints to limit internal stresses due to manufacturing tolerances, yet this paper shows clearly that manufacturing imperfections can still result in significantly different dynamic behaviour.

Designing hybrid flexure systems and elements using Freedom and Constraint Topologies

In this paper we introduce the principles necessary to synthesize hybrid flexure systems and elements. Flexure systems consist of rigid bodies that are joined together by flexure elements that elastically deform to guide the system's rigid bodies with desired degrees of freedom (DOFs). The principles introduced here for synthesizing hybrid flexure systems and elements are extensions of the Freedom and Constraint Topologies (FACT) synthesis approach. FACT utilizes a comprehensive library of geometric shapes from which designers can rapidly consider and compare a multiplicity of flexure concepts that achieve any desired set of DOFs. Prior to this paper, designers primarily used these shapes to synthesize parallel and serial flexure systems and elements. With this paper, designers may now use these same shapes to synthesize more general flexures that consist of various combinations of parallel and serial systems and elements (i.e., hybrid configurations). As such, designers can access a larger body of flexure solutions that satisfy demanding design requirements. Instructions for helping designers utilize or avoid the advantages and challenges of over-, under-, and exact-constraint are also provided. Hybrid systems and elements are analysed and designed as case studies.

Exact Constraint Design of a Two-Degree of Freedom Flexure-Based Mechanism1

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; Grüblers 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.