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J. Mechanisms Robotics. 2016;9(1):011001-011001-7. doi:10.1115/1.4035085.

In a foregoing publication, the authors studied pentapods with mobility 2, where neither all the platform anchor points nor all the base anchor points are located on a line. It turned out that the given classification is incomplete. This article is devoted to the discussion of the missing cases resulting in additional solutions already known to Duporcq.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;9(1):011002-011002-7. doi:10.1115/1.4035087.

This paper presents a five degrees-of-freedom (DoF) low inertia shoulder exoskeleton. This device is comprised of two novel technologies. The first is 3DoF spherical parallel manipulator (SPM), which was developed using a new method of parallel manipulator design. This method involves mechanically coupling certain DoF of each independently actuated linkage of the parallel manipulator in order to constrain the kinematics of the entire system. The second is a 2DoF passive slip interface used to couple the user upper arm to the SPM. This slip interface increases system mobility and prevents joint misalignment caused by the translational motion of the user's glenohumeral joint from introducing mechanical interference. An experiment to validate the kinematics of the SPM was performed using motion capture. The results of this experiment validated the SPM's forward and inverse kinematic solutions through an Euler angle comparison of the actual and command orientations. A computational slip model was created to quantify the passive slip interface response for different conditions of joint misalignment. In addition to offering a low inertia solution for the rehabilitation or augmentation of the human shoulder, this device demonstrates a new method of motion coupling, which can be used to impose kinematic constraints on a wide variety of parallel architectures. Furthermore, the presented device demonstrates a passive slip interface that can be used with either parallel or serial robotic systems.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;9(1):011003-011003-10. doi:10.1115/1.4035188.

This paper presents a classification of 3T1R parallel manipulators (PMs) based on the wrench graph. By using the theory of reciprocal screws, the properties of the three-dimensional projective space, the wrench graph, and the superbracket decomposition of Grassmann–Cayley algebra, six typical wrench graphs for 3T1R parallel manipulators are obtained along with their singularity conditions. Furthermore, this paper shows a way in which each of the obtained typical wrench graphs can be used in order to synthesize new 3T1R parallel manipulator architectures with known singularity conditions and with an understanding of their geometrical properties and assembly conditions.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;9(1):011004-011004-6. doi:10.1115/1.4035086.

Various plants have the ability to follow the sun with their flowers or leaves via a mechanism known as heliotropism, which is powered by pressure gradients between neighboring motor cells. Adapting this bio-inspired mechanism, in this paper we present a novel origami-inspired pneumatic solar tracking system for a picosatellite named NPU-PhoneSat that is capable of solar tracking without altering the attitude of the NPU-PhoneSat. We give an overview of the system design and address the theoretical problem of modeling the origami-inspired pneumatic solar tracking system. The theoretical results are compared with the experimental data, demonstrating the validity of the proposed analytical model. Such understanding of soft solar trackers will allow their performance to be predicted, thus enabling their wide utilization in enhancing energy supply.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189.

This paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having three joints, each either revolute or prismatic and each with selectable compliance. The geometry of the mechanism and the location of the compliance frame relative to the mechanism base are each arbitrary but specified. Necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. We show that, for an appropriately constructed serial mechanism having at least one revolute joint, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. For each type of three-joint combination, requirements on the redundant mechanism geometry are identified for the realization of every point planar elastic behavior at a given location, just by changing the mechanism configuration and the joint compliances.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;9(1):011006-011006-7. doi:10.1115/1.4035220.

To overcome the constraint of conventional tilted beam-based bistable mechanism, this paper proposes a novel type of bistable structure based on tilted-angle compound parallelogram flexure to achieve a larger stroke of negative stiffness region while maintaining a compact physical size. As an application of the presented bistable mechanism, a flexure constant-force micropositioning stage is designed to deliver a large stroke. The constant force output is obtained by combining a bistable flexure mechanism with a positive-stiffness flexure mechanism. To facilitate the parametric design of the flexure mechanism, analytical models are derived to quantify the stage performance. The models are verified by carrying out nonlinear finite-element analysis (FEA). A metal prototype is fabricated for experimental study. Results demonstrate the effectiveness of the proposed ideas for a long-stroke, constant-force compliant mechanism dedicated to precision micropositioning applications. Experimental results also show the appearance of two-stage constant force due to the manufacturing errors of the bistable beams.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;9(1):011007-011007-10. doi:10.1115/1.4035126.

Redundantly actuated parallel manipulators (PMs) receive growing interest due to their reduced singularity and enlarged workspace. This paper proposes new indices for optimal design and analysis of redundantly actuated PMs by evaluating their motion/force transmissibility. First, we proposed a method to extract a multi-DOF (degrees-of-freedom) redundantly actuated PM into several subsidiary one-DOF PMs with two or more actuators by locking some actuators in an ergodic manner. Then, a new index of output transmission performance is proposed by investigating the mean value of the instantaneous power produced by the multiple actuation wrenches and one twist of the moving platform of one-DOF PMs. A local transmission index (LTI) is defined as the minimum value of the index of output and input transmission performance. A global transmission index (GTI) is then established based on the LTI. The proposed LTI and GTI are coordinate-free and have clear physical interpretation. Finally, the validity and universality of the new indices are demonstrated by optimization and analysis of redundantly actuated lower-mobility PMs with extra articulated six-DOF or limited-DOF limbs.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;9(1):011008-011008-9. doi:10.1115/1.4035221.

In this paper, the wrench accuracy for parallel manipulators is examined under variations in parameters and data. The solution sets of actuator forces/torques are investigated utilizing interval arithmetic (IA). Implementation issues of interval arithmetic to analyze the performance of manipulators are addressed, including the consideration of dependencies in parameters and the design of input vectors to generate the required wrench. Specifically, the effect of the dependency within and among the entries of the Jacobian matrix is studied, and methodologies for reducing and/or eliminating the overestimation of solution set are presented. In addition, the subset of solution set that produces platform wrenches within the required lower and upper bounds is modeled. Furthermore, the formulation of solutions that provide any platform wrench within the defined interval is examined. Intersection of these two sets, if any, results in the given interval platform wrench. Implementation of the methods to identify the solution for actuator forces/torques is presented on example parallel manipulators.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;9(1):011009-011009-13. doi:10.1115/1.4035117.

The leg mechanism of the novel jumping robot, Salto, is designed to achieve multiple functions during the sub-200 ms time span that the leg interacts with the ground, including minimizing impulse loading, balancing angular momentum, and manipulating power output of the robot's series-elastic actuator. This is all accomplished passively with a single degree-of-freedom linkage that has a coupled, unintuitive design which was synthesized using the technique described in this paper. Power delivered through the mechanism is increased beyond the motor's limit by using variable mechanical advantage to modulate energy storage and release in a series-elastic actuator. This power modulating behavior may enable high amplitude, high frequency jumps. We aim to achieve all required behaviors with a linkage composed only of revolute joints, simplifying the robot's hardware but necessitating a complex design procedure since there are no pre-existing solutions. The synthesis procedure has two phases: (1) design exploration to initially compile linkage candidates, and (2) kinematic tuning to incorporate power modulating characteristics and ensure an impulse-limited, rotation-free jump motion. The final design is an eight-bar linkage with a stroke greater than half the robot's total height that produces a simulated maximum jump power 3.6 times greater than its motor's limit. A 0.27 m tall prototype is shown to exhibit minimal pitch rotations during meter high test jumps.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;9(1):011010-011010-9. doi:10.1115/1.4035187.

For special purpose robotic arms, such as a rail mounted ballast-water tank inspection arm, specific needs require special designs. Currently, there is no method to efficiently design robotic arms that can handle not quantifiable requirements. In this paper, an efficient method for the design and evaluation of the kinematics of manipulator arms on mobile platforms, with certain reach requirements within a limited space, is presented. First, the design space for kinematic arm structures is analyzed and narrowed down by a set of design rules. Second, key test locations in the workspace are determined and reduced based on, for example, relative positions and symmetry. Third, an algorithm is made to solve the inverse kinematics problem in an iterative way, using a virtual elastic wrench on the end effector to control the candidate structure toward its desired pose. The algorithm evaluates the remaining candidate manipulator structures for every required end-effector positions in the reduced set. This method strongly reduces the search space with respect to brute force methods and yields a design that is guaranteed to meet specifications. This method is applied to the use case of a rail-guided robot for ballast-water tank inspection. The resulting manipulator design has been built and the proof of concept has been successfully evaluated in a ballast-water tank replica.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;9(1):011011-011011-11. doi:10.1115/1.4035270.

This paper presents an approach to compliance modeling of three-translation and two-rotation (3T2R) overconstrained parallel manipulators, especially for those with multilink and multijoint limbs. The expressions of applied wrenches (forces/torques) exerted on joints are solved with few static equilibrium equations based on screw theory. A systematic method is proposed for deriving the stiffness model of a limb with considering the couplings between the stiffness along the constrained wrench and the one along the actuated wrench based on strain energy analysis. The compliance model of a 3T2R overconstrained parallel mechanism is established based on stiffness models of limbs and the static equilibrium equation of the moving platform. Comparisons show that the compliance matrix obtained from the method is close to the one obtained from a finite-element analysis (FEA) model. The proposed method has the characteristics of involving low computational efforts and considering stiffness couplings of each limb.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(1):011012-011012-9. doi:10.1115/1.4035505.

Robots are rapidly becoming part of our lives, coexisting, interacting, and collaborating with humans in dynamic and unstructured environments. Mapping of human to robot motion has become increasingly important, as human demonstrations are employed in order to “teach” robots how to execute tasks both efficiently and anthropomorphically. Previous mapping approaches utilized complex analytical or numerical methods for the computation of the robot inverse kinematics (IK), without considering the humanlikeness of robot motion. The scope of this work is to synthesize humanlike robot trajectories for robot arm-hand systems with arbitrary kinematics, formulating a constrained optimization scheme with minimal design complexity and specifications (only the robot forward kinematics (FK) are used). In so doing, we capture the actual human arm-hand kinematics, and we employ specific metrics of anthropomorphism, deriving humanlike poses and trajectories for various arm-hand systems (e.g., even for redundant or hyper-redundant robot arms and multifingered robot hands). The proposed mapping scheme exhibits the following characteristics: (1) it achieves an efficient execution of specific human-imposed goals in task-space, and (2) it optimizes anthropomorphism of robot poses, minimizing the structural dissimilarity/distance between the human and the robot arm-hand systems.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(1):011013-011013-9. doi:10.1115/1.4035496.

Sleeve pneumatic muscles have shown significant performance improvements over conventional air muscle design, offering increased energy efficiency, force output, and stroke length, while allowing the actuator to become a structural component. However, there remain comparatively few studies involving sleeve muscles, and current applications have not focused on their potential advantages for joints actuated antagonistically with two muscles or their application to a more general class of pneumatic artificial muscle. This research presents a modular sleeve muscle design using the McKibben type construction, with a separate membrane and braid. To further increase stroke length, an internal pulley mechanism is implemented. The performance of the sleeve muscle is compared to an equivalent unaltered muscle and shows substantial improvements in force output, stroke length, and energy efficiency. Further testing shows that the internal pulley mechanism increased the effective stroke length by 82%, albeit at the cost of reduced maximum force output.

Topics: Muscle , Pulleys , Design
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(1):011014-011014-11. doi:10.1115/1.4035504.

The subject of Bresse's circles is classical in the kinematics of planar mechanisms. These are the loci of the coupler points that exhibit either zero normal or zero tangential acceleration. Described in this paper is the construction of the spherical equivalent of Bresse's circles, which take the form of an inflexion spherical cubic and a Thales ellipse, respectively. An algorithm is developed to produce these loci for the case of the spherical antiparallelogram. As a byproduct, the corresponding polodes and their evolutes are obtained.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(1):011015-011015-9. doi:10.1115/1.4035543.

Aiming at acquiring large deformation capability, powerful strength output, rapid response, and flexible locomotion, a novel three degrees-of-freedoms (DOFs) rolling parallel robot is proposed. This robot adopts the parallel mechanism, and its structure can guarantee the stiffness of the robot. The large capability of deformation can be obtained by taking advantage of the antiparallelogram mechanism with an enlarging mechanism of extension ratio. Hydraulic actuation is used for the telescopic input, which can increase the locomotion flexibility and the strength output of the robot. Rolling motion of the robot can be reached through planning and controlling the relations between the center of mass (CM) of the robot and the supporting region. The mechanical construction and configuration of the robot are described, the rolling gaits are planned, and the optimal locomotion law is given. Based on the law, the kinematic model of the robot is created. The kinematic model is validated by the given numerical example. The locomotion feasibility of two locomotion periods is analyzed. A set of experimental tests on the hydraulic system and the robotic system are performed. Results of four rolling experiments verify the reliability of the experimental system and the rapid response capability and also verify the validity and feasibility of the theoretical analysis and the rolling locomotion.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(1):011016-011016-7. doi:10.1115/1.4035222.

I have designed a sequence of gravity-powered passive-dynamic toys. These explore locomotion in general and hopping in particular. As with walking, running, crawling, etc., for animals, locomotion in these devices is a horizontal translation by means of approximately periodic patterns of motion. These toys were developed using intuitively guided trial-and-error design iteration based on live viewing, sound sequences, and review of slow motion video. A series of statically stable mechanisms is described. A progression of designs led to the central result: a monopod hopper that repeatedly hops more than 70 steps down a ramp, without conventional feedback control, fast spinning parts, or sensing means, yet unlike the previously statically stable designs, it cannot stand still stably. This free hopping was facilitated by a special mass distribution, and a spring that allowed relative translation and rotation between the body and leg. A retrospective evaluation reveals similarities to the morphology and gaits of hopping bipeds. These toys, interesting dynamical systems in any case, highlight the possibility of a significant role of mechanical structure in locomotion.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(1):011017-011017-13. doi:10.1115/1.4035337.

We have experimented with and simulated Steinkamp's passive-dynamic hopper. This hopper cannot stand up (it is statically unstable), yet it can hop the length of a 5 m 0.079 rad sloped ramp, with n100 hops. Because, for an unstable periodic motion, a perturbation Δx0 grows exponentially with the number of steps (ΔxnΔx0×λn), where λ is the system eigenvalue with largest magnitude, one expects that if λ>1 that the amplification after 100 steps, λ100, would be large enough to cause robot failure. So, the experiments seem to indicate that the largest eigenvalue magnitude of the linearized return map is less than one, and the hopper is dynamically stable. However, two independent simulations show more subtlety. Both simulations correctly predict the period of the basic motion, the kinematic details, and the existence of the experimentally observed period 11 solutions. However, both simulations also predict that the hopper is slightly unstable (|λ|max>1). This theoretically predicted instability superficially contradicts the experimental observation of 100 hops. Nor do the simulations suggest a stable attractor near the periodic motion. Instead, the conflict between the linearized stability analysis and the experiments seems to be resolved by the details of the launch: a simulation of the hand-holding during launch suggests that experienced launchers use the stability of the loosely held hopper to find a motion that is almost on the barely unstable limit cycle of the free device.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Mechanisms Robotics. 2016;9(1):014501-014501-8. doi:10.1115/1.4035084.

A fixed-guided beam, with one end is fixed while the other is guided in that the angle of that end does not change, is one of the most commonly used flexible segments in compliant mechanisms such as bistable mechanisms, compliant parallelogram mechanisms, compound compliant parallelogram mechanisms, and thermomechanical in-plane microactuators. In this paper, we split a fixed-guided beam into two elements, formulate each element using the beam constraint model (BCM) equations, and then assemble the two elements' equations to obtain the final solution for the load–deflection relations. Interestingly, the resulting load–deflection solution (referred to as Bi-BCM) is closed-form, in which the tip loads are expressed as functions of the tip deflections. The maximum allowable axial force of Bi-BCM is the quadruple of that of BCM. Bi-BCM also extends the capability of BCM for predicting the second mode bending of fixed-guided beams. Besides, the boundary line between the first and the second modes bending of fixed-guided beams can be easily obtained using a closed-form equation. Bi-BCM can be immediately used for quick design calculations of compliant mechanisms utilizing fixed-guided beams as their flexible segments (generally no iteration is required). Different examples are analyzed to illustrate the usage of Bi-BCM, and the results show the effectiveness of the closed-form solution.

Commentary by Dr. Valentin Fuster

Design Innovation Paper

J. Mechanisms Robotics. 2017;9(1):015001-015001-10. doi:10.1115/1.4035495.

Robotic reduction of long bones is associated with the need for considerable force and high precision. To balance the accuracy, payload, and workspace, we have designed a new six degrees-of-freedom three-legged wide-open robotic system for long-bone fracture reduction. Thanks to the low number of legs and their nonsymmetrical configuration, the mechanism enjoys a unique architecture with a frontally open half-plane. This facilitates positioning the leg inside the mechanism and provides a large workspace for surgical maneuvers, as shown and compared to the well-known Gough–Stewart platform. The experimental tests on a phantom reveal that the mechanism is well capable of applying the desired reduction steps against the large muscular payloads with high accuracy.

Commentary by Dr. Valentin Fuster

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