Research Papers

J. Mechanisms Robotics. 2017;10(1):011001-011001-10. doi:10.1115/1.4038530.

In this paper, we propose a variable width compliant link that is designed for optimal trade-off of safety and control performance for inherently safe corobots. Intentionally introducing compliance to mechanical design increases safety of corobots. Traditional approaches mostly focus on the joint compliance, while few of them study the link compliance. Here, we propose a novel method to design compliant robotic links with a safety constraint which is quantified by head injury criterion (HIC). The robotic links are modeled as two-dimensional beams with a variable width. Given a safety threshold, i.e., HIC constraint, the width distribution along the link is optimized to give a uniform distribution of HIC, which guarantees inherent safety for human operators. This solution is validated by a human–robot impact simulation program built in matlab. A static model of the variable width link is derived and verified by finite element simulations. Not only stress in the link is reduced, this new design has a better control and dynamic performance quantified by a larger natural frequency and a larger bandwidth compared with designs made of uniform beams and compliant joints (CJs). The proposed variable width link takes full advantage of the link rigidity while keeps inherent safety during a human–robot impact. This paper demonstrates that the compliant link solution could be a promising alternative approach for addressing safety concerns of human–robot interactions.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;10(1):011002-011002-8. doi:10.1115/1.4038440.

With the proliferation of successful minimally invasive surgical techniques, comes the challenge of shrinking the size of surgical instruments further to facilitate use in applications such as neurosurgery, pediatric surgery, and needle procedures. This paper introduces laser machined, multi-degree-of-freedom (DOF) hinge joints embedded on tubes, as a possible means to realize such miniature instruments without the need for any assembly. A method to design such a joint for an estimated range of motion was explored. The effects of design and machining parameters on the mechanical interference, range of motion, and joint dislocation were analyzed. The extent of interference between the moving parts of the joint can be used to predict the range of motion of the joint for rigid tubes and future design optimization. The total usable workspace was also estimated using kinematic principles for a joint in series and for two sets of orthogonal joints. Our work can open up avenues to a new class of miniature robotic medical devices with hinge joints and a usable channel for drug delivery.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;10(1):011003-011003-10. doi:10.1115/1.4038305.

This paper studies the problem of spherical four-bar motion synthesis from the viewpoint of acquiring circular geometric constraints from a set of prescribed spherical poses. The proposed approach extends our planar four-bar linkage synthesis work to spherical case. Using the image space representation of spherical poses, a quadratic equation with ten linear homogeneous coefficients, which corresponds to a constraint manifold in the image space, can be obtained to represent a spherical RR dyad. Therefore, our approach to synthesizing a spherical four-bar linkage decomposes into two steps. First, find a pencil of general manifolds that best fit the task image points in the least-squares sense, which can be solved using singular value decomposition (SVD), and the singular vectors associated with the smallest singular values are used to form the null-space solution of the pencil of general manifolds; second, additional constraint equations on the resulting solution space are imposed to identify the general manifolds that are qualified to become the constraint manifolds, which can represent the spherical circular constraints and thus their corresponding spherical dyads. After the inverse computation that converts the coefficients of the constraint manifolds to the design parameters of spherical RR dyad, spherical four-bar linkages that best navigate through the set of task poses can be constructed by the obtained dyads. The result is a fast and efficient algorithm that extracts the geometric constraints associated with a spherical motion task, and leads naturally to a unified treatment for both exact and approximate spherical motion synthesis.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;10(1):011004-011004-10. doi:10.1115/1.4038684.

An appropriate choice of contact forces for anthropomorphic robotic grasping devices is important for achieving a balanced grasp. Too little applied force may cause an object to slip or be dropped, and too much applied force may cause damage to delicate objects. Prior methods of grasping force optimization (GFO) in the literature can be difficult to compare due to variability in the parameters, such as the type of grasping device, the object grasped, and the contact model, among other factors. Additionally, methods are typically tested on a very small number of scenarios and may not be as robust in other settings. This paper presents a detailed analysis of three optimization approaches based on the literature, comparing them on the basis of accuracy and computational efficiency. Numerical examples are provided for three types of grasp commonly performed by the human hand (cylindrical grasp, tip grasp, and tripod grasp) using both soft finger (SF) contact and hard finger (HF) contact friction models. For each method and grasping example, an external force is applied to the object in eighteen different directions to provide a more complete picture of the methods' performance. Contact points between the hand and the object are predetermined (given). A comparison of the results showed that the nonlinear and linear matrix inequality (LMI) approaches perform best in terms of accuracy, while the computational efficiency of the linear method is stronger unless the number of contact points and segments becomes too large. In this case, the nonlinear method performs more quickly. Future work will extend the problem of GFO to real-time implementation, and a related work (briefly addressed here) examines the sensitivity of optimization methods to variability in the contact locations.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;10(1):011005-011005-7. doi:10.1115/1.4038529.

This paper designs a one degree-of-freedom (1DOF) spatial flapping wing mechanism for a hovering micro-air vehicle by constraining a spatial RRR serial chain using two SS dyads. The desired wing movement defines the dimensions and joint trajectories of the RRR spatial chain. Seven configurations of the chain are selected to define seven precision points that are used to compute SS chains that control the swing and pitch joint angles. The result is a spatial RRR-2SS flapping wing mechanism that transforms the actuator rotation into control of wing swing and pitch necessary for hovering flight of a micro-air vehicle.

Topics: Chain , Design , Wings , Vehicles
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;10(1):011006-011006-9. doi:10.1115/1.4038527.

This paper focuses on parallel mechanisms (PMs) that can perform two translations and two rotations (2T2R). Two sufficient conditions for eliminating parasitic motion in 2T2R PMs are presented. A motion expression satisfying those two conditions is identified and several kinematic bonds containing that motion are found. To achieve symmetrical structures, a configurable platform that generates an instantaneous translation motion is presented, to which four limbs having identical structures are connected, leading to the construction of novel 2T2R PMs. Several designs that may have good practical values are identified and form a mechanism family. A typical mechanism is selected with its position model, workspace, singularity thoroughly investigated. Redundant limbs are added to eliminate the singularities, which then ensure the rotational capability. The proposed mechanisms have the advantages of identical limbs, no parasitic motion, and relatively high rotational capability, which can be used in several applications such as in five-axis machine.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;10(1):011007-011007-11. doi:10.1115/1.4038441.

A method for validating rigid-body models of compliant mechanisms under dynamic loading conditions using motion tracking cameras and genetic algorithms is presented. The compliant mechanisms are modeled using rigid-body mechanics as compliant joints (CJ): spherical joints with distributed mass and three-axis torsional spring dampers. This allows compliant mechanisms to be modeled using computationally efficient rigid-body dynamics methods, thereby allowing a model to determine the desired stiffness and location characteristics of compliant mechanisms spatially distributed into a structure. An experiment was performed to validate a previously developed numerical dynamics model with the goal of tuning unknown model parameters to match the flapping kinematics of the leading edge spar of an ornithopter with contact-aided compliant mechanisms (CCMs), compliant mechanisms that feature self-contact to produce nonlinear stiffness, inserted. A system of computer motion tracking cameras was used to record the kinematics of reflective tape and markers placed along the leading edge spar with and without CCMs inserted. A genetic algorithm was used to minimize the error between the model and experimental marker kinematics. The model was able to match the kinematics of all markers along the spars with a root-mean-square error (RMSE) of less than 2% of the half wingspan over the flapping cycle. Additionally, the model was able to capture the deflection amplitude and harmonics of the CCMs with a RMSE of less than 2 deg over the flapping cycle.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;10(1):011008-011008-13. doi:10.1115/1.4038528.

Kinematic singularities of linkages are configurations where the differential mobility changes. Constraint singularities are critical points of the constraint mapping defining the loop closure constraints. Configuration space (c-space) singularities are points where the c-space ceases to be a smooth manifold. These singularity types are not identical and can neither be distinguished nor identified by simply investigating the rank deficiency of the constraint Jacobian (linear dependence of joint screws). C-space singularities are reflected by the c-space geometry. In a previous work, a kinematic tangent cone was introduced as an approximation of the c-space, defined as the set of tangents to smooth curves in c-space. Identification of kinematic singularities amounts to analyze the local geometry of the set of critical points. As a computational means, a kinematic tangent cone to the set of critical points is introduced in terms of Jacobian minors. Closed form expressions for the derivatives of the minors in terms of Lie brackets of joint screws are presented. A computational method is introduced to determine a polynomial system defining the kinematic tangent cone. The paper complements the recently proposed mobility analysis using the tangent cone to the c-space. This allows for identifying c-space and kinematic singularities as long as the solution set of the constraints is a real variety. The introduced approach is directly applicable to the higher-order analysis of forward kinematic singularities of serial manipulators. This is briefly addressed in the paper.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;10(1):011009-011009-9. doi:10.1115/1.4038648.

This paper proposes a probabilistic approach for the design of elastic elements to be used in structure-controlled variable stiffness actuators (VSA) for robotic applications. Considering the natural dynamics of the elastic actuation system, requirements are defined and material selection as well as geometry calculation are performed using lumped parameter models. Monte Carlo simulations are integrated in the design procedure to ensure a robust implementation of the required dynamical characteristics. Thereby, effects of uncertainties that might be caused by manufacturing or deviations of material properties are taken into account. To validate the suitability of the overall approach and the particular methods, a torsional elastic element is implemented and experimentally evaluated. The evaluation shows a fulfillment of the key requirements, i.e., specific natural dynamic behavior, that is only achieved due to considering uncertainties. Further, the transferability of the approach to other structure-controlled elastic actuators is discussed and implications are given. Only the governing equations of stiffness properties in certain load situation need to be adapted, e.g., from torsion to bending. Due to the simple transfer, the proposed probabilistic and model-based approach is promising for application to various actuator concepts with structure-controlled variable stiffness.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;10(1):011010-011010-10. doi:10.1115/1.4038685.

The radial folding ratio of single-vertex multicrease rigid origami, from the folded configuration to the unfolded configuration, is satisfactory. In this study, we apply two approaches to add nonzero thickness for this kind of origami and identify different geometrical characteristics. Then, the model of the secondary folding origami, which can help to further decrease the folding ratio, is constructed. We apply the method of constraining the edges of the panels on prescribed planes to geometrically obtain the kinematic model. Based on the kinematic model and the screw theory, the nonzero thickness origami is transformed into the deployable mechanism with one degree-of-freedom (1DOF). Other similar mechanisms can be derived based on this basic configuration. The computer-aided design examples are presented to indicate the feasibility.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;10(1):011011-011011-11. doi:10.1115/1.4038306.

The subject of this paper is twofold: the kinematics and the isotropic design of six degrees-of-freedom (DOF), three-CCC parallel-kinematics machines (PKMs). Upon proper embodiment and dimensioning, the PKMs discussed here, with all actuators mounted on the base, exhibit interesting features, not found elsewhere. One is the existence of an isotropy locus, as opposed to isolated isotropy points in the workspace, thereby guaranteeing the accuracy and the homogeneity of the motion of the moving platform (MP) along different directions within a significantly large region of their workspace. The conditions leading to such a locus are discussed in depth; several typical isotropic designs are brought to the limelight. Moreover, the kinematic analysis shows that rotation and translation of the MP are decoupled, which greatly simplifies not only the kinetostatic analysis but also, most importantly, their control. Moreover, it is shown that the singularity loci of this class of mechanism are determined only by the orientation of their MP, which also simplifies locus evaluation and eases its representation.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Mechanisms Robotics. 2017;10(1):014501-014501-6. doi:10.1115/1.4038220.

In this work, we present a closed-form model, which describes the kinematics of fiber-reinforced elastomeric enclosures (FREEs). A FREE actuator consists of a thin elastomeric tube surrounded by reinforcing helical fibers. Previous models for the motion of FREEs have relied on the successive compositions of “instantaneous” kinematics or complex elastomer models. The model presented in this work classifies each FREE by the ratio of the length of its fibers. This ratio defines the behavior of the FREE regardless of the other parameters. With this ratio defined, the kinematic state of the FREE can then be completely described by one of the fiber angles. The simple, analytic nature of the model presented in this work facilitates the understanding and design of FREE actuators. We demonstrate the application of this model in an actuator design case study.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;10(1):014502-014502-8. doi:10.1115/1.4038219.

This paper presents a novel mechanism of tree climbing robotic system for tree pruning. The unique features of this system include the passive and active anti-falling mechanisms, which prevent the robot from falling to the ground under either static or dynamic situations, the capability to vertically or spirally climb up a tree trunk, and the flexibility to suit different trunk sizes. The computer-aided design (CAD) models of the robotic mechanism, static and kinematic analysis, climbing simulation, and testing of the physical model are stated in detail. This research work reveals that this novel tree climbing mechanism can be served as a platform for tree pruning robot.

Topics: Robots , Wheels , Design , Robotics
Commentary by Dr. Valentin Fuster

Design Innovation Paper

J. Mechanisms Robotics. 2017;10(1):015001-015001-12. doi:10.1115/1.4038254.

This work presents a novel miniature contact-aided compliant joint mechanism that can be integrated into millimeter-sized manual or robotic surgical instruments. The design aims to address the trade-off between notched-tube compliant joints' range of motion and stiffness, while also ensuring a compact form factor. The mechanism is constructed from a nitinol tube with asymmetric cutouts and is actuated in bending by a cable. The innovative feature of this design is the incorporation of a contact aid into the notched-tube topology, which acts to both increase the stiffness of the joint and change the shape that it undertakes during bending. Using finite element modeling (FEM) techniques, we present a sensitivity analysis investigating how the performance of this contact-aided compliant mechanism (CCM) is affected by its geometry, and derive a kinematics and statics model for the joint. The FEM simulations and the kinematic and static models are compared to experimental results. The design and modeling presented in this study can be used to develop new miniature dexterous instruments, with a particular emphasis on applications in minimally invasive neurosurgery.

Commentary by Dr. Valentin Fuster

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