Compliant Mechanical Systems Research Articles

Multiscale Topology Optimization of modulated fluid microchannels based on asymptotic homogenization

Dehomogenization techniques are becoming increasingly popular for enhancing lattice designs of compliant mechanical systems with ultra-large resolutions. Their effectiveness hinges on computing a deformed periodic grid that enable to reconstruct fine-scale designs with modulated and oriented patterns. In this paper, we propose an approach for extending dehomogenization methods to laminar fluid systems. We initiate our methodology by asymptotically deriving Darcy’s law on a periodically porous medium deformed by a diffeomorphism. Unlike the mechanical context, we reveal that the homogenized permeability matrix depends not solely on local the orientation but also on the local dilation of the deformed periodic medium. This distinction presents one of the several challenges to be tackled when adapting dehomogenization-based topology optimization techniques to porous media. To accommodate existing methodologies, we formulate a simplified “poor man’s” homogenized model, which streamlines various aspects, yet still leans on periodic cell problems to estimate the spatially varying permeability matrix. Specifically, we overlook boundary layer effects, we presume periodic grid deformations, and we neglect local dilation, solely considering the relationship with local cell orientations. Subsequently, we present a numerical approach for designing a system that redistributes an input flow across numerous regularly spaced outlets at an output interface. Leveraging the homogenized model, we deduce optimized geometric arrangements of local channel spacing parameters and orientations. We then use established methods to reconstruct grid deformations and fine-scale designs. The fidelity of these reconstructions is then validated through fine-scale simulations. Our observations indicate that while the proposed designs yield satisfactory performance when subjected to the full-scale model, discernible deviations from the homogenized model persist, appealing to future improvements.

A harmonic balance approach for designing compliant mechanical systems with nonlinear periodic motions

We present a computational method for designing compliant mechanical systems that exhibit large-amplitude oscillations. The technical core of our approach is an optimization-driven design tool that combines sensitivity analysis for optimization with the Harmonic Balance Method for simulation. By establishing dynamic force equilibrium in the frequency domain, our formulation avoids the major limitations of existing alternatives: it handles nonlinear forces, side-steps any transient process, and automatically produces periodic solutions. We introduce design objectives for amplitude optimization and trajectory matching that enable intuitive high-level authoring of large-amplitude motions. Our method can be applied to many types of mechanical systems, which we demonstrate through a set of examples involving compliant mechanisms, flexible rod networks, elastic thin shell models, and multi-material solids. We further validate our approach by manufacturing and evaluating several physical prototypes.

Energy shaping control of an inverted flexible pendulum fixed to a cart

Control of compliant mechanical systems is increasingly being researched for several applications including flexible link robots and ultra-precision positioning systems. The control problem in these systems is challenging, especially with gravity coupling and large deformations, because of inherent underactuation and the combination of lumped and distributed parameters of a nonlinear system. In this paper we consider an ultra-flexible inverted pendulum on a cart and propose a new nonlinear energy shaping controller to keep the pendulum at the upward position with the cart stopped at a desired location. The design is based on a model, obtained via the constrained Lagrange formulation, which previously has been validated experimentally. The controller design consists of a partial feedback linearization step followed by a standard PID controller acting on two passive outputs. Boundedness of all signals and (local) asymptotic stability of the desired equilibrium is theoretically established. Simulations and experimental evidence assess the performance of the proposed controller.

Load speed regulation in compliant mechanical transmission systems using feedback and feedforward control actions

The problem of controlling the load speed of a mechanical transmission system consisting of a belt-pulley and gear-pair is considered. The system is modeled as two inertia (motor and load) connected by a compliant transmission. If the transmission is assumed to be rigid, then using either the motor or load speed feedback provides the same result. However, with transmission compliance, due to belts or long shafts, the stability characteristics and performance of the closed-loop system are quite different when either motor or load speed feedback is employed. We investigate motor and load speed feedback schemes by utilizing the singular perturbation method. We propose and discuss a control scheme that utilizes both motor and load speed feedback, and design an adaptive feedforward action to reject load torque disturbances. The control algorithms are implemented on an experimental platform that is typically used in roll-to-roll manufacturing and results are shown and discussed.

Blended Linear Models for Reduced Compliant Mechanical Systems.

We present a method for the simulation of compliant, articulated structures using a plausible approximate model that focuses on modeling endpoint interaction. We approximate the structure's behavior about a reference configuration, resulting in a first order reduced compliant system, or FORK (-1) S. Several levels of approximation are available depending on which parts and surfaces we would like to have interactive contact forces, allowing various levels of detail to be selected. Our approach is fast and computation of the full structure's state may be parallelized. Furthermore, we present a method for reducing error by combining multiple FORK (-1)S models at different linearization points, through twist blending and matrix interpolation. Our approach is suitable for stiff, articulate grippers, such as those used in robotic simulation, or physics-based characters under static proportional derivative control. We demonstrate that simulations with our method can deal with kinematic chains and loops with non-uniform stiffness across joints, and that it produces plausible effects due to stiffness, damping, and inertia.

Energy Shaping Methods for Asymptotic Force Regulation of Compliant Mechanical Systems

In this brief, we address the robust force regulation problem of mechanical systems in physical interaction with compliant environments. The control method that we present is entirely derived under the energy shaping framework. Note that for compliant interactions, standard energy shaping methods (i.e., potential shaping controls using static-state feedback actions) cannot guarantee asymptotic stability since they are not robust to unmodeled forces. To cope with this issue, in this brief, we integrate force sensory feedback with a robust energy shaping design. This methodology allows us to incorporate integral force controls while preserving in closed loop the port-Hamiltonian structure, something that is not possible with traditional force regulators. We discuss the practical implementation of our method and provide simple numerical algorithms to compute in real time some of its control terms. To validate our approach, we report an experimental study with an open architecture robot manipulator.

Stochastic switching of cantilever motion

The cantilever is a prototype of a highly compliant mechanical system and has an instrumental role in nanotechnology, enabling surface microscopy, and ultrasensitive force and mass measurements. Here we report fluctuation-induced transitions between two stable states of a strongly driven microcantilever. Geometric nonlinearity gives rise to an amplitude-dependent resonance frequency and bifurcation occurs beyond a critical point. The cantilever response to a weak parametric modulation is amplified by white noise, resulting in an optimum signal-to-noise ratio at finite noise intensity. This stochastic switching suggests new detection schemes for cantilever-based instrumentation, where the detection of weak signals is mediated by the fluctuating environment. For ultrafloppy, cantilevers with nanometer-scale dimensions operating at room temperature--a new transduction paradigm emerges that is based on probability distributions and mimics nature.

Design of Electrothermally Compliant MEMS With Hexagonal Cells Using Local Temperature and Stress Constraints

In this paper, meso- and microscale electrothermally compliant mechanical systems are synthesized for strength, with polysilicon as the structural material. Local temperature and/or stress constraints are imposed in the topology optimization formulation. This is done to keep the optimal solutions thermally intact and also to keep the local stresses below their allowable limit. Constraint relaxation performed on both temperature and stress constraints allows them to be ignored when the cell material densities approach their nonexisting states. As both local constraints are large in number with the number of cells, an active constraint strategy is employed with gradient based optimization. Honeycomb parametrization, which is a staggered arrangement of hexagonal cells, is used to represent the design region. This ensures at least an edge connection between any two adjacent cells, and thus prevents the appearance of both checkerboard and point flexure singularities without any additional computational load. Both SIMP and SIGMOID material assignment functions are explored to obtain the optimal solutions.

Static equilibrium analysis of compliant mechanical systems using relative coordinates and loop closure equations

This paper deals with the static equilibrium formulation of mechanical systems, including rigid and compliant elements, and the determination of their final equilibrium configuration under known loads. Statically determinate as well as statically indeterminate systems are analysed. Relative coordinates are used as generalised coordinates. The system is modeled using homogeneous transformation matrices and loop closure equations. In the first phase of analysis (assembly), initial correct configuration of the system is obtained, from approximate input provided by the user. For the solution of the equilibrium problem, a potential function is used. Its minimisation, subject to rigid constraints yields the equilibrium configuration. The approach is implemented in a program and tested on a number of planar and spatial mechanical systems. The software program is intended to be used as a design aid for engineers.