Anupam Saxena

Synthesis of Compliant Mechanisms for Path Generation using Genetic Algorithm

In this paper is described a procedure to synthesize the optimal topology, shape, and size of compliant continua for a given nonlinear output path. The path is prescribed using a finite number of distinct precision points much in accordance with the synthesis for path generation in traditional kinematics. Geometrically nonlinear analysis is employed to model large displacements of the constituent members. It is also essential to employ nonlinear analysis to allow the output port to negotiate the prescribed path accurately. The topology synthesis problem is addressed in its original binary form in that the corresponding design variables are only allowed to assume values of 0 for no material and 1 for the material present at a site in the design region. Shape and size design variables are modeled using continuous functions. Owing to the discrete nature of topology design variables, since gradient based optimization methods cannot be employed, a genetic algorithm is used that utilizes only the objective values to approach an optimum solution. A notable advantage of a genetic algorithm over its gradient based counterparts is the implicit circumvention of nonconvergence in the large displacement analysis, which is another reason why a genetic algorithm is chosen for optimization. The least squared objective is used to compare the design and desired output responses. To allow a user to specify preference for a precision point, individual multiple least squared objectives, same in number as the precision points are used. The multiple objectives are solved using Nondominated Sorting in Genetic Algorithm (NSGA-II) to yield a set of pareto optimal solutions. Thus, multiple solutions for compliant mechanisms can be obtained such that a mechanism can traverse one or some precision points among those specified more precisely. To traverse the entire path, a solution that minimizes the sum of individual least square objectives may be chosen. Synthesis examples are presented to demonstrate the usefulness of the proposed method that is capable of generating a solution that can be manufactured as is without requiring any interpretation.

A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments

Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads. Because of this fact, traditional methods of deflection analysis do not apply. Since the nonlinearities introduced by these large deflections make the system comprising such members difficult to solve, parametric deflection approximations are deemed helpful in the analysis and synthesis of compliant mechanisms. This is accomplished by representing the compliant mechanism as a pseudo-rigid-body model. A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms. In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads. A numerical integration technique using quadrature formulae has been employed to solve the large deflection Bernoulli-Euler beam equation for the tip deflection. Implementation of this scheme is simpler than the elliptic integral formulation and provides very accurate results. An example for the synthesis of a compliant mechanism using the proposed model is also presented.

Synthesis of Path Generating Compliant Mechanisms Using Initially Curved Frame Elements

Initially curved frame elements are used in this paper within an optimization-based framework for the systematic synthesis of compliant mechanisms (CMs) that can trace nonlinear paths. These elements exhibit a significantly wider range of mechanical responses to applied loads than the initially straight frame elements, which have been widely used in the past for the synthesis of CMs. As a consequence, fewer elements are required in the design discretization to obtain a CM with a desired mechanical response. The initial slopes at the two nodes of each element are treated as design variables that influence not only the shape of the members in a CM, but also the mechanical response of the latter. Building on our prior work, the proposed synthesis approach uses genetic algorithms with both binary (i.e., 0/1) and continuous design variables in conjunction with a co-rotational total Lagrangian finite element formulation and a Fourier shape descriptors-based objective function. This objective function is chosen for its ability to provide a robust comparison between the actual path traced by a candidate CM design and the desired path. Two synthesis examples are presented to demonstrate the synthesis procedure. The resulting designs are fabricated as is, without any postprocessing, and tested. The fabricated prototypes show good agreement with the design intent.

A Material-Mask Overlay Strategy for Continuum Topology Optimization of Compliant Mechanisms Using Honeycomb Discretization

This paper proposes novel honeycomb tessellation and material-mask overlay methods to obtain optimal single-material compliant topologies free from checkerboard and point-flexure pathologies. The presence of strain-free rotation regions in rectangular cell based discretization is identified to be a cardinal cause for appearance of such singularities. With each hexagonal cell sharing an edge with its neighboring cells, strain-free displacements are not permitted anywhere in the continuum. The new material assignment approach manipulates material within a subregion of cells as opposed to a single cell thereby reducing the number of variables making optimization efficient. Cells are allowed to get filled with only the chosen material or they can remain void. Optimal solutions obtained are free from intermediate material states and can be manufactured requiring no material interpretation and less postprocessing. Though the hexagonal cells do not allow strain-free rotations, some subregions undergoing large strain deformations can still be present within the design. The proposed procedure is illustrated using three classical examples in compliant mechanisms solved using genetic algorithm.

Beyond Parameter Estimation: Extending Biomechanical Modeling by the Explicit Exploration of Model Topology

Selecting a model topology that realistically predicts biomechanical function remains an unsolved problem. Todays dominant modeling approach is to replicate experimental input/output data by performing parameter estimation on an assumed topology. In contrast, we propose that modeling some complex biomechanical systems requires the explicit and simultaneous exploration of model topology (i.e., the type, number, and organization of physics-based functional building blocks) and parameter values. In this paper, we use the example of modeling the notoriously complex tendon networks of the fingers to present three critical advances towards the goal of implementing this extended modeling paradigm. First, we describe a novel computational environment to perform quasi-static simulations of arbitrary topologies of elastic structures undergoing large deformations. Second, we use this form of simulation to show that the assumed topology for the tendon network of a finger plays an important role in the propagation of tension to the finger joints. Third, we demonstrate the use of a novel inference algorithm that simultaneously explores the topology and parameter values for hidden synthetic tendon networks. We conclude by discussing critical issues of observability, separability, and uniqueness of topological features inferred from input/output data, and outline the challenges that need to be overcome to apply this novel modeling paradigm to extract causal models in real anatomical systems.

An Improved Material-Mask Overlay Strategy for Topology Optimization of Structures and Compliant Mechanisms

The honeycomb-based domain representation directly yields checkerboard and point flexure free optimal solutions to various topology design problems without requiring any supplementary suppression method. This is because the root cause behind the appearance of these pathologies, namely, the permitted single-point connectivity between contiguous subregions in rectangular-cell-based representation, is eliminated. The mesh-free material-mask overlay method further promises unadulterated “black and white” solutions in contrast to density interpolation schemes where the material is modeled between the “void” and “filled” states. Here, we propose improvements to the material-mask overlay method by judiciously increasing the number of material masks during a sequence of subsearches for the best solution. We used an alternative, mutation-based zero-order stochastic search, which, through a small population of solution vectors, can yield multiple solutions from a single search for nonconvex topology optimization formulations. Wachspress hexagonal cells are used as finite elements since they offer rich displacement interpolation functions. Singular solutions are penalized and filtered. With the improved material-mask overlay method, we showcase the synthesis using two classical small displacement problems each on optimal stiff structures and compliant mechanisms to illustrate the extraction of pathology-free, “black and white,” and multiple solutions. DOI: 10.1115/1.4001530

Control of an optimal finger exoskeleton based on continuous joint angle estimation from EMG signals

Patients suffering from loss of hand functions caused by stroke and other spinal cord injuries have driven a surge in the development of wearable assistive devices in recent years. In this paper, we present a system made up of a low-profile, optimally designed finger exoskeleton continuously controlled by a users surface electromyographic (sEMG) signals. The mechanical design is based on an optimal four-bar linkage that can model the fingers irregular trajectory due to the fingers varying lengths and changing instantaneous center. The desired joint angle positions are given by the predictive output of an artificial neural network with an EMG-to-Muscle Activation model that parameterizes electromechanical delay (EMD). After confirming good prediction accuracy of multiple finger joint angles we evaluated an index finger exoskeleton by obtaining a subjects EMG signals from the left forearm and using the signal to actuate a finger on the right hand with the exoskeleton. Our results show that our sEMG-based control strategy worked well in controlling the exoskeleton, obtaining the intended positions of the device, and that the subject felt the appropriate motion support from the device.

On Honeycomb Parameterization for Topology Optimization of Compliant Mechanisms

Discrete parameterization using full or partial ground structures of truss/frame elements is not appropriate for domain representation as they do not map all points in the continuum and can lead to dangling or overlapping elements in the optimal topology. Existing continuum parameterization using units cells with holes, ranked microstructures or penalized Young’s modulus (SIMP model) mainly have problems like the appearance of checkerboard patterns and stiffness singularity regions. This is probably due to point-contact between diagonally placed cells and such regions can be avoided by using higher order elements, perimeter constraints or filtering schemes which result in additional computational load on the optimization procedures. An edge connectivity throughout is ensured when using a honeycomb representation with staggered regular hexagonal cells. In this paper, such a parameterization is employed for topology synthesis of compliant mechanisms with flexibility-stiffness and flexibility-strength multi-criteria formulations. The material connectivity is well-defined, and checkerboard and zero-stiffness singularities are not seen in numerous examples solved with honeycomb parameterization.Copyright

On Multiple-Material Optimal Compliant Topologies: Discrete Variable Parameterization Using Genetic Algorithm

Ideally, topology design problems are posed in binary form wherein density-like parameters, that model material properties, assume values corresponding to either no material or material state at a point in the continuum. However, to facilitate the use of calculus-based algorithms, which rely on gradient information for their search, the densities are often relaxed and posed as continuous interpolating functions between the two states. An alternative is to employ an algorithm that uses only the function information as its search criteria while strictly maintaining the original binary form. Genetic algorithm, which simulates nature’s mechanism of natural selection and survival of the fittest, is employed in this paper for topology optimization of compliant mechanisms. The algorithm is capable of converging to a global optimum, and therefore, is additionally beneficial as the design spaces for compliant mechanisms are often multi-modal. During the search, a barrier assignment approach is employed for densities to assume values corresponding only to the material or no material states. A cardinal advantage is the generalization to multiple-material modeling that enables suitable juxtaposition of flexible and stiff material in optimal compliant topology design and is supplemented well by modern manufacturing techniques. Numerous synthesis examples are solved, both with two and multiple material models, to illustrate the efficacy of the proposed method for the design of compliant continua. The approach is generic and can be employed to any topology design problem at hand and with any finite element approximation to the continuum.Copyright

Trajectory Generation Using GA for an 8 DOF Biped Robot with Deformation at the Sole of the Foot

In biped robot dynamics, the foot is generally considered rigid. However, in practical cases, there will be a layer of rubber on the sole to act as a shock absorber. Such electrodynamic contact has been studied in the case of industrial robots, but the experience with biped robots is rare. The goal of this paper is to device a trajectory generation method using a genetic algorithm (GA) for an 8 DOF robot that can walk on flat terrain and climb stairs with deformation at the sole. The proposed method uses splines to model each joint angle and needs a single GA layer, which makes it faster and simpler than earlier models. The method incorporates the dynamics of an actual 8 DOF robot to find the most energy optimal gait. A simple control method is proposed that corrects the computed angle required to follow ZMP incorporating the deformation of the sole. Using the control method the computed angle is first corrected and then the trajectory optimized. Energy consumed in three cases were compared: walk on flat ground with no sole deformation, walk with uncorrected deformed soft sole and walk with deformed soft sole with correction of deformation. It is found that the least energy was consumed in the case of soft sole with correction for deformation. This proves the need for deformation correction of soft sole and the usefulness of our proposed method.