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Research Papers

J. Mechanisms Robotics. 2018;11(1):011001-011001-10. doi:10.1115/1.4041485.

This paper introduces the design of a specific landing gear retraction system presenting a mechanism with four redundant side stays and examines its dynamic behavior during the folding and unfolding processes. First, a concept design of a four-side-stay landing gear retraction system is presented. To get the particular motion during folding and unfolding, the main kinematics parameters are given. Then, the influence of the side stay's kinematic redundancy on the mechanism parameters is examined. Because the mechanism is overconstrained, the allowable parameters belong to a specific region of the space called feasible region. Finally, a dynamic analysis of the over-constrained system is executed by using the Newton–Euler approach and compliant equations. Numerical simulations indicate that this kind of landing gear retraction system equitably share the loads between different side stays, and therefore, the total load at one side stay is greatly reduced.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011002-011002-10. doi:10.1115/1.4041585.

Understanding and analyzing large and nonlinear deflections are the major challenges of designing compliant mechanisms. Initially, curved beams can offer potential advantages to designers of compliant mechanisms and provide useful alternatives to initially straight beams. However, the literature on analysis and design using such beams is rather limited. This paper presents a general and accurate method for modeling large planar deflections of initially curved beams of uniform cross section, which can be easily adapted to curved beams of various shapes. This method discretizes a curved beam into a few elements and models each element as a circular-arc beam using the beam constraint model (BCM), which is termed as the chained BCM (CBCM). Two different discretization schemes are provided for the method, among which the equal discretization is suitable for circular-arc beams and the unequal discretization is for curved beams of other shapes. Compliant mechanisms utilizing initially curved beams of circular-arc, cosine and parabola shapes are modeled to demonstrate the effectiveness of CBCM for initially curved beams of various shapes. The method is also accurate enough to capture the relevant nonlinear load-deflection characteristics.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011003-011003-14. doi:10.1115/1.4041584.

We propose a novel hybrid robot with seven degrees-of-freedom (DOF) and variable topology for operation in space. Design specifications of the space robot are presented for the type synthesis of hybrid mechanisms. Based on GF set theory, three design rules are given, thus providing the design method of the 7DOF hybrid space robot mechanism. Twenty-four combinations of the hybrid robotic mechanisms are obtained. The final synthesized configuration for the design of the space robot has a 3DOF parallel module and a 4DOF serial module with four revolute (RRRR) joints. The parallel module consists of a limb with universal-prismatic (UP) joints and two limbs with universal-prismatic-spherical (UPS) joints. The topology of the hybrid robot can be changed, and it will become an RPRR four-bar mechanism when it is folded for launch. The closed-form solution for the inverse displacement model is developed, and then the forward displacement equations are also obtained. After that, the Jacobian matrix is derived from the displacement model; the Jacobian matrix will analyze the singularity and workspace. We find that there are four singularities of mechanisms. The dexterous workspace of the hybrid robot is a good match for the grapple operation in space. An experiment with the prototype shows the present hybrid robot can grapple to a satellite-rocket docking ring and therefore validates the kinematic equations.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011004-011004-15. doi:10.1115/1.4041486.

Reconfiguration identification of a mechanism is essential in design and analysis of reconfigurable mechanisms. However, reconfiguration identification of a multiloop reconfigurable mechanism is still a challenge. This paper establishes the first- and second-order kinematic model in the queer-square mechanism to obtain the constraint system by using the sequential operation of the Lie bracket in a bilinear form. Introducing a bilinear form to reduce the complexity of first- and second-order constraints, the constraint system with first- and second-order kinematics of the queer-square mechanism is attained in a simplified form. By obtaining the solutions of the constraint system, six motion branches of the queer-square mechanism are identified and their corresponding geometric conditions are presented. Moreover, the initial configuration space of the mechanism is obtained.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011006-011006-11. doi:10.1115/1.4041631.

This paper addresses the problem of discretizing the curved developable surfaces that are satisfying the equivalent surface curvature change discretizations. Solving basic folding units occurs in such tasks as simulating the behavior of Gauss mapping. The Gauss spherical curves of different developable surfaces are setup under the Gauss map. Gauss map is utilized to investigate the normal curvature change of the curved surface. In this way, spatial curved surfaces are mapped to spherical curves. Each point on the spherical curve represents a normal direction of a ruling line on the curved surface. This leads to the curvature discretization of curved surface being transferred to the normal direction discretization of spherical curves. These developable curved surfaces are then discretized into planar patches to acquire the geometric properties of curved folding such as fold angle, folding direction, folding shape, foldability, and geometric constraints of adjacent ruling lines. It acts as a connection of curved and straight folding knowledge. The approach is illustrated in the context of the Gauss map strategy and the utility of the technique is demonstrated with the proposed principles of Gauss spherical curves. It is applicable to any generic developable surfaces.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011007-011007-8. doi:10.1115/1.4041632.

Soft linear actuators (SLAs) such as shape memory alloy (SMA) wires, pneumatic soft actuators, dielectric elastomer actuator, and twisted and coiled soft actuator (TCA) called artificial muscle actuators in general, have many advantages over the conventional actuators. SLAs can realize innovative robotic technologies like soft robots, wearable robots, and bionic arms in the future, but further development is still needed in real applications because most SLAs do not provide large displacement or force as needed. This paper presents a novel mechanism supplementing SLAs by accumulating the displacement of multiple SLAs. It adopts the principle of differential gears in reverse. Since the input units of the mechanism are extensible, more displacement can be accumulated by increasing the number of the input units as many as needed. The mechanism is basically used to accumulate displacements, but can be used to accumulate forces by changing its operating mode. This paper introduces the design and working principle of the mechanism and validates its operation experimentally. In addition, the mechanism is implemented on a robotic arm and its effectiveness is confirmed.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011008-011008-8. doi:10.1115/1.4041698.

This paper presents a novel kinematically redundant planar parallel robot manipulator, which has full rotatability. The proposed robot manipulator has an architecture that corresponds to a fundamental truss, meaning that it does not contain internal rigid structures when the actuators are locked. This also implies that its rigidity is not inherited from more general architectures or resulting from the combination of other fundamental structures. The introduced topology is a departure from the standard 3-RPR (or 3-RRR) mechanism on which most kinematically redundant planar parallel robot manipulators are based. The robot manipulator consists of a moving platform that is connected to the base via two RRR legs and connected to a ternary link, which is joined to the base by a passive revolute joint, via two other RRR legs. The resulting robot mechanism is kinematically redundant, being able to avoid the production of singularities and having unlimited rotational capability. The inverse and forward kinematics analyses of this novel robot manipulator are derived using distance-based techniques, and the singularity analysis is performed using a geometric method based on the properties of instantaneous centers of rotation. An example robot mechanism is analyzed numerically and physically tested; and a test trajectory where the end effector completes a full cycle rotation is reported. A link to an online video recording of such a capability, along with the avoidance of singularities and a potential application, is also provided.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011009-011009-9. doi:10.1115/1.4041586.

Compliant kaleidocycles can be widely used in a variety of applications, including deployable structures, origami structures, and metamorphic robots, due to their unique features of continuous rotatability and multistability. Inspired by origami kaleidocycles, a type of symmetric multistable compliant mechanism with an arbitrary number of units is presented and analyzed in this paper. First, the basic dimension constraints are developed based on mobility analysis using screw theory. Second, the kinematic relationships of the actual rotation angle are obtained. Third, a method to determine the number of stabilities and the position of stable states, including the solution for the parameterized boundaries of stable regions, is developed. Finally, experimental platforms are established, and the validity of the proposed multistable mechanisms is verified.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011010-011010-12. doi:10.1115/1.4041739.

Continuum robots are becoming increasingly popular due to the capabilities they offer, especially when operating in cluttered environments, where their dexterity, maneuverability, and compliance represent a significant advantage. The subset of continuum robots that also belong to the soft robots category has seen rapid development in recent years, showing great promise. However, despite the significant attention received by these devices, various aspects of their kinematics remain unresolved, limiting their adoption and obscuring their potential. In this paper, the kinematics of continuum robots with the ability to bend and extend are studied, and analytical, closed-form solutions to both the direct and inverse kinematics are presented. The results obtained expose the redundancies of these devices, which are subsequently explored. The solution to the inverse kinematics derived here is shown to provide an analytical, closed-form expression describing the curve associated with these redundancies, which is also presented and analyzed. A condition on the reachable end-effector poses for robots with six actuation degrees-of-freedom (DOFs) is then distilled. The kinematics of robot layouts with over six actuation DOFs are subsequently considered. Finally, simulated results of the inverse kinematics are provided, verifying the study.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011011-011011-11. doi:10.1115/1.4041785.

Compliant shell mechanisms utilize spatially curved thin-walled structures to transfer or transmit force, motion, or energy through elastic deformation. To design spatial mechanisms, designers need comprehensive nonlinear characterization methods, while the existing methods fall short of meaningful comparisons between rotational and translational degrees-of-freedom. This paper presents two approaches, both of which are based on the principle of virtual loads and potential energy, utilizing properties of screw theory, Plücker coordinates, and an eigen-decomposition. This leads to two unification lengths that can be used to compare and visualize all six degrees-of-freedom directions and magnitudes in a nonarbitrary, physically meaningful manner for mechanisms exhibiting geometrically nonlinear behavior.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011012-011012-9. doi:10.1115/1.4041941.

In minimally invasive surgery (MIS), surgeons often suffer from occlusion region problems. It is difficult to solve these problems with traditional surgical instruments because of their size and rigid mechanical structure, such as endoscopes and corresponding operating tools. Thus, flexible manipulators and related robotic systems have been proposed for enhancing intraoperative inspection and surgical operation in MIS. Although a variety of flexible manipulators using different mechanisms have been developed, most of them are designed with a single function. In this paper, we present the concept of visible forceps that enriches the forceps function, which realizes the flexible bending capability and high output force, as well as the integrated endoscopic function. We developed a novel simplified linkage bending mechanism for forceps with a bendable tip and fabricated a robotic visible forceps manipulator system. According to this prototype, we performed experiments to evaluate the mechanical performance and the abdominal phantom test to evaluate the feasibility and usefulness. Preliminary results show that the forceps manipulator can realize both flexible bending capability and high output force, which implies promising applications in future MIS.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011013-011013-9. doi:10.1115/1.4041641.

Among Bricard's overconstrained 6R linkages, the third type has two collapsed configurations, where all joint axes are coplanar. This paper presents a one-degree-of-freedom network of such linkages. Using the two coplanar states of the constituent Bricard units, the network is able to cover a large surface with a specific outline when deployed and can be folded compactly into a stack of much smaller planar shapes. Five geometric parameters describing each type III Bricard mechanism are introduced. Their influence on the outline of one collapsed configuration is discussed and inverse calculation to obtain the parameter values yielding a desired planar shape is performed. The network is built by linking the units, either using scissor linkage elements, if the thickness of the panels can be ignored, or with hinged parallelograms, for a thicker material. Two case studies, in which the Bricard network deploys as a rectangle and a regular hexagon, respectively, are presented, validating the analysis and design methods.

Topics: Linkages , Shapes
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011014-011014-9. doi:10.1115/1.4041697.

Propulsive capability of manta rays' flapping pectoral fins has inspired many to incorporate these fins as propulsive mechanisms for autonomous underwater vehicles. In particular, geometrical factors such as sweep angle have been postulated as being influential to these fins' propulsive capability, specifically their thrust generation. Although effects of sweep angle on static/flapping wings of aircrafts/drones have been widely studied, little has been done for underwater conditions. Furthermore, the findings from air studies may not be relatable to the underwater studies on pectoral fins because of the different Reynolds number (compared to the flapping wings) and force generation mechanism (compared to the static wings). This paper aims to establish a relationship between the sweep angle and thrust generation. An experiment was conducted to measure the thrust generated by 40 fins in a water channel under freestream and still water conditions for chord Reynolds number between 2.2 × 104 and 8.2 × 104. The fins were of five different sweep angles (0 deg, 10 deg, 20 deg, 30 deg, and 40 deg) that were incorporated into eight base designs of different flexibility characteristics. The results showed that the sweep angle (within the range considered) may have no significant influence on these fins' thrust generation, implying no significant effects on thrust under uniform flow condition and on the maximum possible thrust under still water. Overall, it can be concluded that sweep angle may not be a determinant of thrust generation for flapping pectoral fins. This knowledge can ease the decision-making process of design of robots propeled by these fins.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):011015-011015-14. doi:10.1115/1.4041789.

This work presents a lightweight soft rehabilitation glove that integrates finger and wrist function by developing and applying the double-DOF soft pneumatic bending actuators (DPBAs). The proposed soft glove can achieve separate as well as coordinated motion exercises of fingers and the wrist, which benefits stroke patients who have complicated hand impairment. It consists of a commercial glove extended by a customized wrist bracer, on which are installed three dorsal DPBAs through fingers (index/middle/ring) and the wrist, two dorsal single-DOF pneumatic bending actuators (SPBAs) through thumb/pinky, and three palmar SPBAs through wrist. The proposed DPBA has two independent bendable segments to actuate flexion of finger and wrist, respectively, whose multigait bending conforms with multipattern flexion of the biological hand. The SPBAs are used for actuating wrist extension or finger flexion. The proposed wrist bracer is designed as an extension of the glove to install the soft actuators and transfer their motion and force to the wearer's wrist efficiently as well as minimize unactuated restriction on the hand. To verify its feasibility, we evaluate the range of motion (ROM), strength and speed of five subjects' hands assisted by the glove in six different passive motions. Results show that the proposed glove can provide sufficient assistance for stroke patients in hand rehabilitation exercise. Furthermore, the soft glove has potential in extending the hand functional training from simple exercises such as closing/opening and gripping to complex ones such as weightlifting, writing, and screwing/unscrewing.

Topics: Actuators , Design , Testing
Commentary by Dr. Valentin Fuster

Technical Brief

J. Mechanisms Robotics. 2018;11(1):014501-014501-5. doi:10.1115/1.4041630.

In this paper, we propose a novel type of soft robot for sit to stand (STS) training, which is made with soft bellow actuators. Analysis with five healthy human subjects revealed that there is a statistically significant decrease in the peak and mean muscle activation signal from three out of the four groups of lower limb muscle for STS transition, namely, tibialis anterior, hamstrings, and quadriceps. The peak muscle activation decreased most drastically on the quadriceps muscle group (0.726 ± 0.467 to 0.269 ± 0.334). As reduced muscle activation signal correlates to less muscular effort required by the users, the results show the effectiveness of the device in partially supporting the STS transition of the subject, which subsequently serves as an STS trainer device.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):014502-014502-6. doi:10.1115/1.4041787.

Flexure pivots are frequently applied in long stroke compliant mechanisms to transmit motion continuously. To improve the motion accuracy, a kind of variable thickness flexure pivot (VTFP) is proposed in this paper. A nonlinear beam element is proposed by utilizing the corotational approach to model the static response of the VTFP under end loads. Finite element analysis and experimental tests are carried out to verify the effectiveness of the modeling method. Based on the static deformation model, the motion range, the rotation stiffness, the center shift, and the variation of the center shift under axial force of the VTFP are investigated. The results show that the VTFP has better motion accuracy and better ability to resist axial force compared with the conventional flexure pivot.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):014503-014503-4. doi:10.1115/1.4041633.

This work seeks to systematically model and solve the equations associated with the kinematics of spherical mechanisms. The group of special unitary matrices, SU(2), is utilized throughout. Elements of SU(2) are employed here to analyze the three-roll wrist and the spherical Watt I linkage. Additionally, the five orientation synthesis of a spherical four-bar mechanism is solved, and solutions are found for the eight orientation synthesis of the Watt I linkage. Using SU(2) readily allows for the use of a homotopy-continuation-based solver, in this case Bertini. The use of Bertini is motivated by its capacity to calculate every solution to a design problem.

Topics: Kinematics , Linkages
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):014504-014504-7. doi:10.1115/1.4041788.

This paper studies the problem of spatial linkage synthesis for motion generation from the perspective of extracting geometric constraints from a set of specified spatial displacements. In previous work, we have developed a computational geometric framework for integrated type and dimensional synthesis of planar and spherical linkages, the main feature of which is to extract the mechanically realizable geometric constraints from task positions, and thus reduce the motion synthesis problem to that of identifying kinematic dyads and triads associated with the resulting geometric constraints. The proposed approach herein extends this data-driven paradigm to spatial cases, with the focus on acquiring the point-on-a-sphere and point-on-a-plane geometric constraints which are associated with those spatial kinematic chains commonly encountered in spatial mechanism design. Using the theory of kinematic mapping and dual quaternions, we develop a unified version of design equations that represents both types of geometric constraints, and present a simple and efficient algorithm for uncovering them from the given motion.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;11(1):014505-014505-8. doi:10.1115/1.4041786.

This paper presents a novel design for a robotic end effector. In particular, the design features a multifingered underactuated gripper capable of performing parallel and self-adaptive (PASA) grasping. The unique use of an eccentric cam fixed to a modified four-bar linkage mechanism allows the finger to compensate for the typical gap distance found during parallel pinching, improving the ability to grasp objects against surfaces and in tight spaces. A static analysis is performed on the design to determine the equilibrium conditions necessary for a successful grasp using this design in both the PASA modes. The mechanics of a four-bar mechanism are used to determine the grasp velocity and positioning of the hand in both grasp modes. Experimental results with a finger prototype confirm the desired closing trajectory.

Commentary by Dr. Valentin Fuster

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