Showing papers in "Journal of Mechanisms and Robotics in 2013"

Solving the Robot-World/Hand-Eye Calibration Problem Using the Kronecker Product

Abstract: This paper constructs a separable closed-form solution to the robot-world/hand-eye calibration problem AX1⁄4YB. Qualifications and properties that determine the uniqueness of X and Y as well as error metrics that measure the accuracy of a given X and Y are given. The formulation of the solution involves the Kronecker product and the singular value decomposition. The method is compared with existing solutions on simulated data and real data. It is shown that the Kronecker method that is presented in this paper is a reliable and accurate method for solving the robot-world/hand-eye calibration problem. [DOI: 10.1115/1.4024473]

Type Synthesis of 3-DOF Parallel Manipulators With Both a Planar Operation Mode and a Spatial Translational Operation Mode

Abstract: Type synthesis of multimode parallel manipulators (PMs) (also parallel manipulators with multiple operation modes) is an open issue in the research on reconfigurable mechanisms and robots. This paper deals with the type synthesis of 3-DOF (degree-of-freedom) parallel manipulators with both a planar operation mode and a spatial translational operation mode. The type synthesis of planar parallel manipulators, which refer to parallel manipulators in which the moving platform undergoes planar motion, is first dealt with using the virtual-chain approach. Types of planar parallel manipulators, including those involving Bennett compositional unit (CU), are obtained. Then, the types of 3-DOF parallel manipulators with both a planar operation mode and a translational operation mode are obtained. This paper focuses on 3-DOF parallel manipulators composed of only revolute joints. This work contributes to the type synthesis of parallel manipulators and can be extended to the type synthesis of other classes of multimode parallel manipulators.

Variable Stiffness Legs for Robust, Efficient, and Stable Dynamic Running

Abstract: Humans and animals adapt their leg impedance during running for both internal (e.g., loading) and external (e.g., surface) changes. To date, the mechanical complexity of designing usefully robust tunable passive compliance into legs has precluded their implementation on practical running robots. This work describes the design of novel, structure-controlled stiffness legs for a hexapedal running robot to enable runtime modification of leg stiffness in a small, lightweight, and rugged package. As part of this investigation, we also study the effect of varying leg stiffness on the performance of a dynamical running robot. For more information: Kod*Lab Comments BibTeX entry @article{Galloway-Journal_of_Mechanisms_and_Robots-2013, author = {Kevin C. Galloway and Jonathan E. Clark et al}, title = {Variable Stiffness Legs for Robust, Efficient, and Stable Dynamic Running}, booktitle = { Journal of Mechanisms and Robotics}, year = {2013}, month = { January}, } This work was partially supported by the NSF FIBR Grant #0425878 and the IC Postdoctoral Fellow Program under Grant no. HM158204–1−2030. This journal article is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/664 Variable Stiffness Legs for Robust, Efficient, and Stable Dynamic Running Kevin C. Galloway Wyss Institute for Biologically Inspired Engineering Harvard University Cambridge, MA 02138 Email: kevin.galloway@wyss.harvard.edu Jonathan E. Clark Department of Mechanical Engineering FAMU/FSU College of Engineering Tallahassee, FL 32310 Email: clarkj@eng.fsu.edu Daniel E. Koditschek GRASP Laboratory Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia, PA, 19104 Email: kod@seas.upenn.edu Humans and animals adapt their leg impedance during running for both internal (e.g. loading) and external (e.g. surface) changes. To date the mechanical complexities of designing usefully robust tunable passive compliance into legs has precluded their implementation on practical running robots. This work describes the design of novel, structure-controlled stiffness legs for a hexapedal running robot to enable runtime modification of leg stiffness in a small, lightweight, and rugged package. As part of this investigation, we also study the effect of varying leg stiffness on the performance of a dynamical running robot.

Unified Kinematics and Singularity Analysis of a Metamorphic Parallel Mechanism With Bifurcated Motion

Abstract: This paper introduces a new metamorphic parallel mechanism consisting of four reconfigurable rTPS limbs. Based on the reconfigurability of the reconfigurable Hooke (rT) joint, the rTPS limb has two phases while in one phase the limb has no constraint to the platform, in the other it constrains the spherical joint center to lie on a plane. This results in the mechanism to have ability of reconfiguration between different topologies with variable mobility. Geometric constraint equations of the platform rotation matrix and translation vector are set up based on the point-plane constraint, which reveals the bifurcated motion property in the topology with mobility 2 and the geometric condition with mobility change in altering to other mechanism topologies. Following this, a unified kinematics limb modeling is proposed considering the difference between the two phases of the reconfigurable rTPS limb. This is further applied for the mechanism modeling and both the inverse and forward kinematics is analytically solved by combining phases of the four limbs covering all the mechanism topologies. Based on these, a unified singularity modeling is proposed by defining the geometric constraint forces and actuation forces in the Jacobian matrix with their change in the variable topologies in terms of constraint screws. Analysis of workspace with singularity distribution is carried out using this model and corresponding singularity loci are obtained with special singular configurations illustrated. [DOI: 10.1115/1.4024292]

Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra

Abstract: In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

Inverse Geometrico-Static Problem of Underconstrained Cable-Driven Parallel Robots With Three Cables

Abstract: This paper studies under-constrained cable-driven parallel robots with three cables. A major challenge in the study of these manipulators is the intrin- sic coupling between kinematics and statics, which must be dealt with simultaneously. In this contribution, gen- eral elimination procedures are provided that solve the inverse geometrico-static problem with assigned orienta- tion or position. In the former case, the platform orienta- tion is given, whereas the platform position and the cable lengths and tensions must be computed. In the latter case, the platform position is known, whereas the platform ori- entation and the cable lengths and tensions must be cal- culated. These problems are proven to admit up to 1 and 24 real solutions, respectively.

Haptic Hand Exoskeleton for Precision Grasp Simulation

Abstract: This paper outlines the design and the development of a novel robotic hand exoskeleton conceived for haptic interaction in the context of virtual reality and teleoperation applications. The device allows exerting controlled forces on fingertips of the index and thumb of the operator. The new exoskeleton features several design solutions adopted with the aim of optimizing force accuracy and resolution. The use of remote centers of motion mechanisms allows achieving a compact and lightweight design. An improved stiffness of the transmission and reduced requirements for the electromechanical actuators are obtained thanks to a novel principle for integrating speed reduction into torque transmission systems. A custom designed force sensor and integrated electronics are employed to further improve performances. The electro-mechanical design of the device and the experimental characterization are presented.

Automatic Structural Synthesis of the Whole Family of Planar 3-Degrees of Freedom Closed Loop Mechanisms

Abstract: Conception of the kinematic structures with better performance has been a challenging, yet pivotal issue, since the beginning of the design of mechanisms or robots. This paper proposes a systematic method to synthesize and classify automatically all the valid kinematic structures of planar 3-DOF closed loop mechanisms or robots. First, after the structure representation graphs of planar mechanisms or robots are addressed, the unique representation of both contracted graphs and topological graphs is proposed and used to detect isomorphism in the synthesis process. Then the valid atlas database of the contracted graphs for planar 3-DOF closed loop mechanisms or robots up to 16-link is built. Based on the atlas database, an automatic synthesis method is proposed to synthesize all the kinematic structures of planar 3-DOF closed loop mechanisms or robots, and the complete atlas database with all the valid kinematic structures classified for planar 3DOF closed loop mechanisms or robots up to 16-link is established. The creative design of 3-DOF heavy-load hydraulic robots is conducted to show the usefulness of the established atlas database. [DOI: 10.1115/1.4024919]

Design of a Novel Long-Range Inflatable Robotic Arm: Manufacturing and Numerical Evaluation of the Joints and Actuation

Abstract: The aim of this paper is to present the design of a new long-range robotic arm based on an inflatable structure. Inflatable robotics has potential for improved large payload-to-weight ratios, safe collision, and inspection in areas inaccessible to human beings as in nuclear plants. The robot presented here is intended to operate inspection or maintenance missions in critical installation taking care to not collide with its environment. It is made with innovative inflatable joints and an original actuation system. Prototypes of this inflatable manipulator were constructed using two different manufacturing procedures. Using LS-DYNA nonlinear dynamic finite element modeling we have numerically analyzed the specific geometry and dynamical behavior of the resulting joints. The simulations have given insight into understanding the joint bending process and have revealed guidance for optimizing the conception.

Multistable Behaviors of Compliant Sarrus Mechanisms

Abstract: Multistable mechanisms providing spatial motion could be useful in numerous applications; this paper explores the multistable behavior of the overconstrained spatial Sarrus mechanisms with compliant joints (CSMs). The mechanism analysis is simplified by considering it as two submechanisms. The kinetostatics of CSMs have been formulated based on the pseudorigid-body method for compliant members at any combination of joints. The kinetostatic results show that a CSM is capable of exhibiting bistability, tristability, and quadristability. The type of behavior is found to depend on the initial (as-fabricated) position and the relative limit positions of the two submechanisms. Possible applications of multistable CSMs include deployable structures, static balancing of human/robot bodies, and weight compensators.

An Algorithm to Study the Elastodynamics of Parallel Kinematic Machines With Lower Kinematic Pairs

Abstract: In this paper, an algorithm to help designers to integrate the elastodynamics analysis along with the inverse positioning and orienting problems of a parallel kinematic machine (PKM) into a single package is conceived. The proposed algorithm applies concepts from the matrix structural analysis (MSA) and finite element analysis (FEA) to determine the generalized stiffness matrix and the linearized elastodynamics equations of a PKM with only lower kinematic pairs. A PKM is modeled as a system of flexible links and rigid bodies connected by means of joints. Three cases are analyzed to consider the combinations between flexible and rigid bodies in order to find the local stiffness matrices. The latter are combined to obtain the limb matrices and, then, the global stiffness matrix of the whole robotic system. The same nodes coming from the links discretization are considered to include joint masses/inertias into the model. Finally, a case study is proposed to show some feasible applications and to compare results to commercial software for validation.

A Computational Approach for Cam Size Optimization of Disc Cam-Follower Mechanisms With Translating Roller Followers

Abstract: The main objective of this work is to present a computational approach for design optimization of disc cam mechanisms with eccentric translating roller followers For this purpose, the objective function defined here takes into account the three major parameters that influence the final cam size, namely the base circle radius of the cam, the radius of the roller and the offset of the follower Furthermore, geometric constraints related to the maximum pressure angle and minimum radius of curvature are included to ensure good working conditions of the system Finally, an application example is presented and used to discuss the main assumptions and procedure adopted throughout this work

Model Validation of an Octopus Inspired Continuum Robotic Arm for Use in Underwater Environments

Abstract: Octopuses are an example of dexterous animals found in nature. Their arms are flexible, can vary in stiffness, grasp objects, apply high forces with respect to their relatively light weight, and bend in all directions. Robotic structures inspired by octopus arms have to undertake the challenges of a high number of degrees of freedom (DOF), coupled with highly flexible continuum structure. This paper presents a kinematic and dynamic model for underwater continuum robots inspired by Octopus vulgaris. Mass, damping, stiffness, and external forces such as gravity, buoyancy, and hydrodynamic forces are considered in the dynamic model. A continuum arm prototype was built utilizing longitudinal and radial actuators, and comparisons between the simulated and experimental results show good agreement.

Reconfiguration Analysis of a Fully Reconfigurable Parallel Robot

Abstract: This paper presents a new method for the topological reconfiguration of a parallel robot. Using the existing structure of a full six degree-of-freedom parallel robot, limited mobility modes can be realized easily without the need to remove branch modules from the robot structure. Instead, branch modules are reconfigured from an unconstrained-active to a constrained-passive state by means of hybrid active/passive motors and reconfigurable universal-to-revolute joints. In doing so, the robot is capable of assuming a configuration that uses only the degrees-of-freedom required to complete a given task. However, due to the system setup, there are multiple candidate configurations available, each with its own workspace and reach capabilities, thus guidance is needed in selecting the appropriate configuration. An isomorphic and workspace analysis are performed to identify the capabilities of each configuration. To accomplish this, a branch-based mobility analysis, and a parametric kinematic constraint equation are formulated. It is shown that limited mobility modes with different isomorphic configurations can be synthesized automatically with this method.

Design of Underactuated Steerable Electrode Arrays for Optimal Insertions

Abstract: This paper addresses the design of wire actuated steerable electrode arrays for optimal insertions in cochlear implant surgery. These underactuated electrode arrays are treated as continuum robots which have an embedded actuation strand inside their flexible medium. By pulling on the actuation strand, an electrode array assumes a minimum-energy shape. The problems of designing optimal actuation strand placement are addressed in this paper. Based on the elastic modeling of the steerable electrode arrays proposed in this paper, an analytical solution of the strand placement is solved to minimize the shape discrepancy between a bent electrode array and a given target curve defined by the anatomy. Using the solved strand placement inside the steerable electrode array, an optimized insertion path planning with robotic assistance is proposed to execute the insertion process. Later, an optimization algorithm is presented to minimize the shape discrepancy between an inserted electrode array and a given target curve during the whole insertion process. Simulations show a steerable electrode array bending using the elastic model and robot insertion path planning with optimized strand placement. Two experiments have been conducted to validate the elastic model and algorithms.

Double-Young Tristable Mechanisms

Abstract: In this work, we present a new class of tristable mechanism called double Young tristable mechanisms (DYTMs), which connect two prestrained Young bistable mechanisms to create three distinct stable equilibrium positions. A three-degree-of-freedom pseudorigid-body (RPB) model is proposed to accurately predict the kinetostatic behaviors of both Young mechanisms and DYTMs. An optimization-based design method is also presented for DYTMs. Two DYTM prototypes were designed based on the method and machined out of polypropylene sheets. Both of the prototypes exhibit tristability, which demonstrate the feasibility of achieving tristability through connecting two prestrained Young mechanisms. The successful prototyping also indicates that the proposed three degree-of-freedom (3DOF) model is capable of identifying feasible designs for DYTMs.

Stiffness Design for a Spatial Three Degrees of Freedom Serial Compliant Manipulator Based on Impact Configuration Decomposition

Abstract: This paper proposes a method of stiffness design for a spatial Three Degrees of Freedom (3DOF) serial compliant manipulator with the objective of protecting the compliant joint actuators when the manipulator comes up against impact. System dynamic equations of serial compliant manipulators integrated with an impact model are linearized to identify the maximum joint torques in the impact. Based on this, a general procedure is given in which maximum joint torques are calculated with different directions of end-effector velocity and impact normal in the manipulator workspace based on a given magnitude of end-effector velocity. By tuning the stiffness for each compliant joint to ensure the maximum joint torque does not exceed the maximum value of the actuator, candidate stiffness values are obtained to make the compliant actuators safe in all cases. The theory and procedure are then applied to the spatial 3DOF serial compliant manipulator of which the impact configuration is decomposed into a 2DOF planar serial manipulator and a 1DOF manipulator with a 2DOF link based on the linearized impact-dynamic model. Candidate stiffness of the 3DOF serial compliant manipulator is obtained by combining analysis of the 2DOF and 1DOF manipulators. The method introduced in this paper can be used for both planar and spatial compliant serial manipulators.

Investigation on the Effort Transmission in Planar Parallel Manipulators

Abstract: In the design of a mechanism, the quality of effort transmission is a key issue. Traditionally, the effort transmissivity of a mechanism is defined as the quantitative measure of the power flowing effectiveness from the input link(s) to the output link(s). Many researchers have focused their work on the study of the effort transmission in mechanisms and diverse indices have been defined. However, the developed indices have exclusively dealt with the studies of the ratio between the input and output powers and they do not seem to have been devoted to the studies of the admissible reactions in passive joints. However, the observations show that is possible for a mechanism to reach positions in which the transmission indices will have admissible values but the reaction(s) in passive joint(s) can reach excessively high values leading to the breakdown of the mechanism. In the present paper, a method is developed to ensure the admissible values of reactions in passive joints of planar parallel manipulators. It is shown that the increase of reactions in passive joints of a planar parallel manipulator depends not only on the transmission angle but also the position of the instantaneous centre of rotation of the platform. It allows the determination of the maximal reachable workspace of planar parallel manipulators taking into account the admissible reactions in its passive joints. The suggested method is illustrated vie a 5R planar parallel mechanism and a planar 3-RPR parallel manipulator. I Introduction Parallel manipulators have many advantages in terms of acceleration capacities and payload-to-weight ratio [1], but one of their main drawbacks concerns the presence of singularities [2]-[5]. It is known that in the neighbourhood of the singular positions the reactions in joints of a manipulator considerably grow up. In order to have a better understanding of this phenomenon, many researchers have focused their works on the analysis of the effort transmission in parallel manipulators. One of the evident criterions for evaluation of effort transmission is the transmission angle (or pressure angle which is equal to 90 degrees minus the transmission angle) [7]-[9]. The pressure angle is well known for characterizing the transmission quality in lower kinematic pairs, such as cams [10], but this idea was also used for effort transmission analysis in the parallel manipulators [7], [9]. To evaluate the effort transmission quality, several indexes have been introduced. One of the first attempts was proposed in [6]. This paper presents a criterion named the Transmission Index (TI) that is based on transmission wrench screw. The TI varies between 0 and 1. If it is equal to 0, the considered link is in a dead position, i.e. it cannot move anymore. If it is equal to 1, this link has the best static properties. In the same vein as [6], the study [11] generalizes the TI for spatial linkages and defines the Global TI (GTI). The authors also prove that the GTI is equal, for prismatic and revolute joints, to the cosine of the pressure angle. The conditioning index was also proposed [12] for characterizing the quality of transmission between the actuators and the end-effector. This index is based on the Jacobian matrix or its "norm", which relate the actuator velocities (efforts, resp.) to the platform twist (wrench, resp.) by the following relations:  t Jq  and T   w J τ , where J is the Jacobian matrix, t the platform twist, q  the input velocities,  the actuator efforts, and w the wrench applied on the platform. All these indices have been used in many works for design and analysis of parallel mechanisms [14]-[21]. However, it is also known that because of the non homogeneity of the terms of the Jacobian matrix, the conditioning index is not well appropriated for mechanisms having both translational and rotational degrees of freedom (DOF) [13]. Moreover, all the previously mentioned indices do not take into account the real characteristics of the actuators, i.e. the fact that their input efforts are bounded between [-max i  , max i  ] [13]. In order to solve this problem, in study [22] a numerical analysis method has been developed. It has been proposed to characterize the force workspace of robots taking into account a given fixed wrench applied on the platform and actuator efforts comprised in the boundary interval [-max i  , max i  ]. However, this workspace depends on the given direction and norm of the external force/moment and will change with the variation of the applied wrench. Moreover, for many robot applications, the external wrench direction is not known, contrary to its norm. Therefore, in [23], a way to compute the maximal workspace

Optimal Inverse Kinematic Solutions for Redundant Manipulators by Using Analytical Methods to Minimize Position and Velocity Measures

Abstract: Two methods are presented to obtain optimal inverse kinematic solutions for redundant manipulators, according to two different performance criteria stipulated in the position and velocity levels. Both methods are analytical throughout except their final stages, which involve the numerical solution of a simplified minimization problem in a position-level case and the numerical integration of a set of differential equations derived optimally in a velocity-level case. Owing to the analytical nature of the methods, the multiple and singular configurations of the manipulator of concern can be identified readily and studied in detail. The methods are applicable for both serial and parallel redundant manipulators. However, they are demonstrated here for a humanoid manipulator with seven revolute joints. In the demonstrations, the first performance criterion is stipulated in the position level as the minimization of the potential energy. In that case, the optimal inverse kinematic solution is first obtained in the position level for a specified position of the hand. Then, it is compatibly extended to the velocity level for a specified motion of the hand. In the main analytical part of the solution, six of the joint variables are expressed in terms of the selected seventh one. Then, the optimal value of the selected joint variable is determined numerically by a simple one dimensional scanning. The second performance criterion is stipulated in the velocity level as the minimization of the kinetic energy. In that case, the optimal inverse kinematic solution is first obtained in the velocity level and then extended to the position level by integration. The main analytical part of the solution provides an optimally determined set of nonlinear differential equations. These differential equations are then integrated numerically in order to obtain the corresponding solution in the position level. However, the corrections needed to eliminate the numerical integration errors are still obtained analytically. The distinct optimal behaviors of the manipulator according to the mentioned criteria are also illustrated and compared for a duration, in which the hand moves in the same specified way.

A Maneuver Based Design of a Passive-Assist Device for Augmenting Active Joints

Abstract: This paper describes a novel, general methodology for designing a parallel, passiveassist device to augment an active system using optimization based on a known maneuver of the active system. Implementation of the passive-assist device can result in an improvement in system performance with respect to efficiency, reliability, and/or utility. The methodology is demonstrated with a torsional spring designed to minimize energy consumption of a prototypical unmanned ground vehicle robot arm. Initial results indicate that this procedure can reduce maximum required torque by 50% and energy consumed by as much as 25%. The proposed method is experimentally verified and compared to other state-of-the-art design approaches. [DOI: 10.1115/1.4024237]

A Bio-Inspired Condylar Hinge for Robotic Limbs

Abstract: This paper presents a novel condylar hinge for robotic limbs which was inspired by the human knee joint. The ligaments in the human knee joint can be modeled as an inverted parallelogram four-bar mechanism. The knee joint also has a condylar cam mechanism between the femur and tibia bones. The bio-inspired joint mimics the four-bar mechanism and the cam mechanism of the human knee joint. The bio-inspired design has the same desirable features of a human knee joint including compactness, high mechanical advantage, high strength, high stiffness and locking in the upright position. These characteristics are important for robotic limbs where there are often tight space and mass limitations. A prototype hinge joint similar in size to the human knee joint has been designed and tested. Experimental tests have shown that the new condylar hinge joint has superior performance to a pin-jointed hinge in terms of mechanical advantage and stiffness. The prototype hinge has a mechanical advantage that is greater than a pin-jointed hinge by up to 35% which leads to a corresponding reduction in the peak force of the actuator of up to 35% for a squatting movement. The paper also presents a five-step design procedure to produce a combined inverted parallelogram mechanism with a cam mechanism.

A Contact-Aided Compliant Displacement-Delimited Gripper Manipulator

Abstract: A novel, monolithic, contact-aided, displacement-delimited gripper is presented. It is designed to employ contact interactions between its deforming members to delimit the output displacement such that excessive forces on the soft, fragile work-pieces are thwarted. The mechanism is appropriated using the topology, shape, and size optimization algorithm which, in addition to yielding structural details, also determines the interacting members and nature of contact. The symmetric halves of this design can be actuated independently thus rendering it the manipulative capabilities in addition to gripping. A cantilevered flexible “U” structure when introduced between the gripper ports of this mechanism can yield additional benefits in terms of reduced gripping forces. Macroscale Teflon prototype of the mechanism is tested on various work-pieces having different stiffness properties. Using experimentally acquired vision data, reaction loads on the work-pieces and gripper ports are estimated probabilistically by solving a Dirichlet problem for continua undergoing large deformation.

On the Dual-Rod Slider Rocker Mechanism and Its Applications to Tristate Rigid Active Docking

Abstract: The dual-rod slider rocker mechanism is equivalent to two traditional single-rod sliders that share a common rocker, where the sliders translate along two opposite directions. Unlike a single-rod system, the dual-rod mechanism is unique, in the sense that the two sliders do not translate the same distance for the same rocker rotation. In this paper, an optimal kinematic and dynamic analysis of the dual-rod slider rocker mechanism is presented. This analysis is supplemented by an application to modular robotic coupling, in which the mechanism is employed by a torque recirculation scheme to enable three independent modes of operation via a single motor. Simulation, finite element analysis, and experimental results validate the kinematic properties of this mechanism, the rigidity of the proposed docking interface, and its three modes of operation. We conclude that the compactness of the dual-rod mechanism, and its unique kinematic properties, exhibits a broad industrial value for applications where size and weight are a critical design constraint, such as space and mobile robotics. [DOI: 10.1115/1.4023178]

An Analytical Model for Calculating the Workspace of a Flexure Hexapod Nanopositioner

Abstract: This paper presents an analytical model for calculating the workspace of a flexure-based hexapod nanopositioner previously built by the National Institute of Standards and Technology (NIST). This nanopositioner is capable of producing high-resolution motions in six degrees of freedom by actuating linear actuators on a planar tri-stage. However, the workspace of this positioner is still unknown, which limits its uses in practical applications. In this work, we seek to derive a kinematic model for predicting the workspace of such kinds of flexure based platforms by assuming that their workspace is mainly constrained by the deformation of flexure joints. We first study the maximum deformation including bending and torsion angles of an individual flexure joint. We then derive the inverse kinematics and calculation of bending and torsion angles of each wire flexure in the overall mechanism with given position of the top platform center of the hexapod nanopositioner. At last, we compare results with finite element models of the entire platform. This model is beneficial for workspace analysis and optimization for design of compliant parallel mechanisms. [DOI: 10.1115/1.4025041]

Application of Distance Geometry to Tracing Coupler Curves of Pin-Jointed Linkages

Abstract: In general, high-order coupler curves of single-degree-of-freedom plane linkages cannot be properly traced by standard predictor–corrector algorithms due to drifting problems and the presence of singularities. Instead of focusing on finding better algorithms for tracing curves, a simple method that first traces the configuration space of planar linkages in a distance space and then maps it onto the mechanism workspace, to obtained the desired coupler curves, is proposed. Tracing the configuration space of a linkage in the proposed distance space is simple because the equation that implicitly defines this space can be straightforwardly obtained from a sequence of bilaterations, and the configuration space embedded in this distance space naturally decomposes into components corresponding to different combinations of signs for the oriented areas of the triangles involved in the bilaterations. The advantages of this two-step method are exemplified by tracing the coupler curves of a double butterfly linkage.