Shorya Awtar

Characteristics of Beam-Based Flexure Modules

The beam flexure is an important constraint element in flexure mechanism design. Nonlinearities arising from the force equilibrium conditions in a beam significantly affect its properties as a constraint element. Consequently, beam-based flexure mechanisms suffer from performance tradeoffs in terms of motion range, accuracy and stiffness, while benefiting from elastic averaging. This paper presents simple yet accurate approximations that capture the effects of load-stiffening and elastokinematic nonlinearities in beams. A general analytical framework is developed that enables a designer to parametrically predict the performance characteristics such as mobility, over-constraint, stiffness variation, and error motions, of beam-based flexure mechanisms without resorting to tedious numerical or computational methods. To illustrate their effectiveness, these approximations and analysis approach are used in deriving the force-displacement relationships of several important beam-based flexure constraint modules, and the results are validated using finite element analysis. Effects of variations in shape and geometry are also analytically quantified.

Constraint-based design of parallel kinematic XY flexure mechanisms

This paper presents parallel kinematic XY flexure mechanism designs based on systematic constraint patterns that allow large ranges of motion without causing over-constraint or significant error motions. Key performance characteristics of XY mechanisms such as mobility, cross-axis coupling, parasitic errors, actuator isolation, drive stiffness, lost motion, and geometric sensitivity, are discussed. The standard double parallelogram flexure module is used as a constraint building-block and its nonlinear force-displacement characteristics are employed in analytically predicting the performance characteristics of two proposed XY flexure mechanism designs. Fundamental performance tradeoffs, including those resulting from the nonlinear load-stiffening and elastokinematic effects, in flexure mechanisms are highlighted. Comparisons between closed-form linear and nonlinear analyses are presented to emphasize the inadequacy of the former. It is shown that geometric symmetry in the constraint arrangement relaxes some of the design tradeoffs, resulting in improved performance. The nonlinear analytical predictions are validated by means of computational finite element analysis and experimental measurements.

Mechatronic design of a ball-on-plate balancing system

This paper discusses the conception and development of a ball-on-plate balancing system based on mechatronic design principles. Realization of the design is achieved with the simultaneous consideration towards constraints like cost, performance, functionality, extendibility, and educational merit. A complete dynamic system investigation for the ball-on-plate system is presented in this paper. This includes hardware design, sensor and actuator selection, system modeling, parameter identification, controller design and experimental testing. The system was designed and built by students as part of the course Mechatronics System Design at Rensselaer.

Design of a large range XY nanopositioning system

Achieving large motion range (> 1 mm) along with nanometric motion quality (< 10 nm), simultaneously, has been a key challenge in nanopositioning systems. Practical limitations associated with the individual physical components (flexure bearing, actuators, and sensors) and their integration, particularly in the case of multi-axis systems, have restricted the range of current nanopositioning systems to about 100 μm. This paper presents a novel physical system layout, with a parallel-kinematic XY flexure mechanism at its heart, that provides a high degree of decoupling between the two motion axes by avoiding geometric over-constraints, provides actuator isolation that allows the use of large-stroke single-axis actuators, and enables a complementary end-point sensing scheme that employs commonly available sensors. These attributes help achieve an unprecedented 10 mm × 10 mm motion range in the proposed nanopositioning system. Having overcome the physical system design challenges, a dynamic model of proposed nanopositioning system is created and verified via system identification methods. In particular, dynamic non-linearities associated with the large displacements of the flexure mechanism and resulting controls challenges are identified. The physical system is fabricated, assembled, and tested to validate its simultaneous large range and nanometric motion capabilities. Preliminary closed-loop test results, which highlight the potential of this new design configuration, are presented.Copyright

A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Load-Displacement Formulation

To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop qualitative and quantitative understanding of their constraint characteristics in terms of stiffness and error motions. This paper provides a highly generalized yet accurate closed-form parametric load-displacement model for two-dimensional beam flexures, taking into account the nonlinearities arising from load equilibrium applied in the deformed configuration. In particular, stiffness and error motions are parametrically quantified in terms of elastic, load-stiffening, kinematic, and elastokinematic effects. The proposed beam constraint model incorporates a wide range of loading conditions, boundary conditions, initial curvature, and beam shape. The accuracy and effectiveness of the proposed beam constraint model is verified by nonlinear finite elements analysis.

Inverted pendulum systems: Rotary and arm-driven - A mechatronic system design case study

The inverted pendulum, a popular mechatronic application, exists in many different forms. The common thread among these systems is to balance a link on end using feedback control. Two challenging inverted pendulum systems are the rotational and arm-driven systems. The system described in this paper can be transformed from the rotational to the arm-driven configuration by replacing the links and setting the base on its side. It was designed and built by students as part of the course Mechatronic System Design at Rensselaer. This paper presents a summary of a mechatronic system design case study for the rotary inverted pendulum system.

An XYZ Parallel-Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom

We present the constraint-based design of a novel parallel kinematic flexure mechanism that provides highly decoupled motions along the three translational directions (X, Y, and Z) and high stiffness along the three rotational directions (θx , θy , and θz ). The geometric decoupling ensures large motion range along each translational direction and enables integration with large-stroke ground-mounted linear actuators or generators, depending on the application. The proposed design, which is based on a systematic arrangement of multiple rigid stages and parallelogram flexure modules, is analyzed via non-linear finite element analysis. A proof-of-concept prototype of the flexure mechanism is fabricated to validate its large range and decoupled motion capability. The analyses as well as the hardware demonstrate an XYZ motion range of 10 mm × 10 mm × 10 mm. Over this motion range, the non-linear FEA predicts a cross-axis error of less than 3%, parasitic rotations less than 2 mrad, less than 4% lost motion, actuator isolation less than 1.5%, and no perceptible motion direction stiffness variation. Ongoing work includes non-linear closed-form analysis and experimental measurement of these error motion and stiffness characteristics.Copyright

Elastic Averaging in Flexure Mechanisms: A Three-Beam Parallelogram Flexure Case Study

Over-constraint is an important concern in mechanism design because it can lead to a loss in desired mobility. In distributed-compliance flexure mechanisms, this problem is alleviated due to the phenomenon of elastic averaging, thus enabling performance-enhancing geometric arrangements that are otherwise unrealizable. The principle of elastic averaging is illustrated in this paper by means of a multi-beam parallelogram flexure mechanism. In a lumped-compliance configuration, this mechanism is prone to over-constraint in the presence of nominal manufacturing and assembly errors. However, with an increasing degree of distributed-compliance, the mechanism is shown to become more tolerant to such geometric imperfections. The nonlinear load-stiffening and elasto-kinematic effects in the constituent beams have an important role to play in the over-constraint and elastic averaging characteristics of this mechanism. Therefore, a parametric model that incorporates these nonlinearities is utilized in predicting the influence of a representative geometric imperfection on the primary motion stiffness of the mechanism. The proposed model utilizes a beam generalization so that varying degrees of distributed compliance are captured using a single geometric parameter.Copyright

Large Stroke Electrostatic Comb-Drive Actuators Enabled by a Novel Flexure Mechanism

This paper presents in-plane electrostatic comb-drive actuators with stroke as large as 245 μm that is achieved by employing a novel clamped paired double parallelogram (C-DP-DP) flexure mechanism. The C-DP-DP flexure mechanism design offers high bearing direction stiffness Kx while maintaining low motion direction stiffness Ky over a large range of motion direction displacement. The resulting high (Kx/Ky) ratio mitigates the onset of sideways snap-in instability, thereby offering significantly greater actuation stroke compared with existing designs. Further improvement is achieved by reinforcing the individual beams in this flexure mechanism. While the traditional paired double parallelogram (DP-DP) flexure design with comb gap G = 3 μm and flexure beam length L1 = 1 mm results in a 50- μm stroke before snap-in, the reinforced C-DP-DP design with the same comb gap and flexure beam length achieves a stroke of 141 μm. Furthermore, this C-DP-DP flexure design provides a 215- μm stroke with G = 4 μm and a 245-μm stroke with G = 6 μm. The presented work includes closed-form stiffness expressions for the reinforced C-DP-DP flexure, a design procedure for selecting dimensions of the overall comb-drive actuator, microfabrication of some representative actuators, and experimental measurements demonstrating the large stroke.

A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Strain Energy Formulation

The beam constraint model (BCM), presented previously, captures pertinent nonlinearities to predict the constraint characteristics of a generalized beam flexure in terms of its stiffness and error motions. In this paper, a nonlinear strain energy formulation for the beam flexure, consistent with the transverse-direction load-displacement and axial-direction geometric constraint relations in the BCM, is presented. An explicit strain energy expression, in terms of beam end displacements, that accommodates generalized loading conditions, boundary conditions, initial curvature, and beam shape, is derived. Using energy-based arguments, new insight into the BCM is elucidated by fundamental relations among its stiffness, constraint, and energy coefficients. The presence of axial load in the geometric constraint and strain energy expressions—a unique attribute of distributed compliance flexures that leads to the elastokinematic effect—is highlighted. Using the principle of virtual work, this strain energy expression for a generalized beam is employed in determining the load-displacement relations, and therefore constraint characteristics, of a flexure mechanism comprising multiple beams. The benefit of this approach is evident in its mathematical efficiency and succinctness, which is to be expected with the use of energy methods. All analytical results are validated to a high degree of accuracy via nonlinear finite element analysis.