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Research Papers

J. Mechanisms Robotics. 2017;9(5):051001-051001-9. doi:10.1115/1.4037018.

In this paper, the design and implementation of a novel leg–wheel robot called Transleg are presented. Transleg adopts the wire as the transmission mechanism to simplify the structure and reduce the weight. To the best knowledge of the authors, the wire-driven method has never been used in the leg–wheel robots, so it makes Transleg distinguished from the existing leg–wheel robots. Transleg possesses four transformable leg–wheel mechanisms, each of which has two active degrees-of-freedom (DOFs) in the legged mode and one in the wheeled mode. Two actuators driving each leg–wheel mechanism are mounted on the body, so the weight of the leg–wheel mechanism is reduced as far as possible, which contributes to improving the stability of the legged locomotion. Inspired by the quadruped mammals, a compliant spine mechanism is designed for Transleg. The spine mechanism is also actuated by two actuators to bend in the yaw and pitch directions. It will be beneficial to the turning motion in the legged and wheeled modes and the bounding gait in the legged mode. The design and kinematic analyses of the leg–wheel and spine mechanisms are presented in detail. To verify the feasibility of Transleg, a prototype is implemented. The experiments on the motions in the legged and wheeled modes, the switch between the two modes, and the spine motions are conducted. The experimental results demonstrate the validity of Transleg.

Topics: Robots , Wire , Actuators , Design , Wheels , Yaw , Knee , Rotation
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051002-051002-8. doi:10.1115/1.4037111.

Although kinematic analysis of conventional mechanisms is a well-documented fundamental issue in mechanisms and robotics, the emerging reconfigurable mechanisms and robots pose new challenges in kinematics. One of the challenges is the reconfiguration analysis of multimode mechanisms, which refers to finding all the motion modes and the transition configurations of the multimode mechanisms. Recent advances in mathematics, especially algebraic geometry and numerical algebraic geometry, make it possible to develop an efficient method for the reconfiguration analysis of reconfigurable mechanisms and robots. This paper first presents a method for formulating a set of kinematic loop equations for mechanisms using dual quaternions. Using this approach, a set of kinematic loop equations of spatial mechanisms is composed of six polynomial equations. Then the reconfiguration analysis of a novel multimode single-degree-of-freedom (1DOF) 7R spatial mechanism is dealt with by solving the set of loop equations using tools from algebraic geometry. It is found that the 7R multimode mechanism has three motion modes, including a planar 4R mode, an orthogonal Bricard 6R mode, and a plane symmetric 6R mode. Three (or one) R (revolute) joints of the 7R multimode mechanism lose their DOF in its 4R (or 6R) motion modes. Unlike the 7R multimode mechanisms in the literature, the 7R multimode mechanism presented in this paper does not have a 7R mode in which all the seven R joints can move simultaneously.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051003-051003-10. doi:10.1115/1.4037112.

A novel parallel robot, dubbed the SDelta, is the subject of this paper. SDelta is a simpler alternative to both the well-known Stewart–Gough platform (SGP) and current three-limb, full-mobility parallel robots, as it contains fewer components and all its motors are located on the base. This reduces the inertial load on the system, making it a good candidate for high-speed operations. SDelta features a symmetric structure; its forward-displacement analysis leads to a system of three quadratic equations in three unknowns, which admits up to eight solutions, or half the number of those admitted by the SGP. The kinematic analysis, undertaken with a geometrical method based on screw theory, leads to two Jacobian matrices, whose singularity conditions are investigated. Instead of using the determinant of a 6 × 6 matrix, we derive one simple expression that characterizes the singularity condition. This approach is also applicable to a large number of parallel robots whose six actuation wrench axes intersect pairwise, such as all three-limb parallel robots whose limbs include, each, a passive spherical joint. The workspace is analyzed via a geometric method, while the dexterity analysis is conducted via discretization. Both show that the given robot has the potential to offer both large workspace and good dexterity with a proper choice of design variables.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051004-051004-11. doi:10.1115/1.4037113.

The sense of touch has always been challenging to replicate in robotics, but it can provide critical information when grasping objects. Nowadays, tactile sensing in artificial hands is usually limited to using external sensors which are typically costly, sensitive to disturbances, and impractical in certain applications. Alternative methods based on proprioceptive measurements exist to circumvent these issues but they are designed for fully actuated systems. Investigating this issue, the authors previously proposed a tactile sensing technique dedicated to underactuated, also known as self-adaptive, fingers based on measuring the stiffness of the mechanism as seen from the actuator. In this paper, a procedure to optimize the design of underactuated fingers in order to obtain the most accurate proprioceptive tactile data is presented. Since this tactile sensing algorithm is based on a one-to-one relationship between the contact location and the stiffness measured at the actuator, the accuracy of the former is optimized by maximizing the range of values of the latter, thereby minimizing the effect of an error on the stiffness estimation. The theoretical framework of the analysis is first presented, followed by the tactile sensing algorithm, and the optimization procedure itself. Finally, a novel design is proposed which includes a hidden proximal phalanx to overcome shortcomings in the sensing capabilities of the proposed method. This paper demonstrates that relatively simple modifications in the design of underactuated fingers allow to perform accurate tactile sensing without conventional external sensors.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051005-051005-9. doi:10.1115/1.4037254.

This paper deals with the kinematic optimization of a five degrees-of-freedom (DoFs) spatial parallel mechanism with three kinematic chains. Inspired by the structure of the icosahedron, the base of the discussed mechanism has been designed into a compact and light-weight frame. Due to the potential advantages, this mechanism is used as a movable plug-in module in a multi-axis machine center to process large-scale parts with rotary contour surfaces. To derive its optimal parameters, kinematic optimization based on the motion/force transmissibility is carried out. The parameter design space (PDS) is generated first. Then, the performance evaluation index (i.e., local transmission index (LTI)) is derived sequentially. On this basis, the good transmission positioning workspace (GTPW) for a given orientation is defined by constraining the value of LTI with a certain metric. Thereafter, the atlases of the GTPW and the optimal region satisfying the workspace constraint are derived in the PDS. Within this region, a set of optimal parameters without dimension are selected. Consequently, the cuboid workspaces within GTPWs are identified in detail. By using the ratio between required workspace in application and the derived cuboid workspaces, optimal geometric parameters with dimension are derived. Workspace analysis results show that, for an arbitrary orientation between the vertical and horizontal directions, there is always a cuboid workspace within GTPW larger than required workspace. In addition, the orientational capability of the mechanism can reach more than 90 deg, and the flexible 2DoFs rotations can also be realized. The work in this paper is very helpful to the development of a mobile machining module.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051006-051006-10. doi:10.1115/1.4037019.

This paper addresses the passive realization of any selected planar elastic behavior with a parallel or a serial manipulator. Sets of necessary and sufficient conditions for a mechanism to passively realize an elastic behavior are presented. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. The restrictions on the set of elastic behaviors that can be realized with a mechanism are described in terms of acceptable locations of realizable elastic behavior centers. Parallel–serial mechanism pairs that realize identical elastic behaviors (dual elastic mechanisms) are described. New construction-based synthesis procedures for planar elastic behaviors are developed. Using these procedures, one can select the geometry of each elastic component from a restricted space of kinematically allowable candidates. With each selection, the space is further restricted until the desired elastic behavior is achieved.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051007-051007-9. doi:10.1115/1.4037255.

We recently proposed the theoretical idea of a wearable balancing aid, consisting of a set of control moment gyroscopes (CMGs) contained into a backpacklike orthopedic corset. Even though similar solutions have been reported in the literature, important considerations in the synthesis and design of the actuators remained to be addressed. These include design requirements such as aerodynamic behavior of the spinning flywheel, induced dynamics by the wearer's motion, and stresses in the inner components due to the generated gyroscopic moment. In this paper, we describe the design and evaluation of a single CMG, addressing in detail the aforementioned requirements. In addition, given the application of the device in human balance, the design follows the European directives for medical electrical equipment. The developed system was tested in a dedicated balance test bench showing good agreement with the expected flywheel speed, and calculated power requirements in the actuators and output gyroscopic moment. The device was capable of producing a peak gyroscopic moment of approximately 70 N·m with a total CMG mass of about 10 kg.

Topics: Flywheels , Design , Actuators
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051008-051008-8. doi:10.1115/1.4037256.

Parallel robots present singular configurations that divide the operational workspace into several aspects. It was proven that type 2 and leg passive joint twist system (LPJTS) singularities can be crossed with a trajectory respecting a given dynamic criterion. However, the practical implementation of a controller able to track such trajectories is up to now limited to restrictive cases of type 2 singularities crossing. Analyzing the structure of the inverse dynamic model, this paper proposes a global solution allowing the tracking of trajectories respecting the general criterion for any singularity that leads to potential issues of dynamic model degeneracy. The tracking is operated in the robot joint space. Experimental results on a five-bar mechanism showed the controller ability to successfully cross type 2 singularities.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051009-051009-13. doi:10.1115/1.4037114.

The VariLeg is an exoskeleton allowing a paraplegic to walk. It was used for competing on an obstacle course at the first Cybathlon. It integrates an adjustable stiffness in the knee joint to improve the walking performance. However, the adjustable stiffness mechanism (ASM) of the VariLeg is bulky and heavy, which hampers the handling of the exoskeleton. Hence, the choice of an ASM concept that only needs small springs is essential. This study benchmarks six state-of-the-art ASMs regarding their needed energy storage capacity, thus their potential for a high compactness. The benchmark is performed with the requirements of the VariLeg and a second requirements set, which can be fulfilled by all six ASMs. The benchmark can be transferred to other requirements as well. It is based on models of the ASMs with their design parameters optimized for the given requirements set. The benchmark reveals large differences between the performances of the investigated ASM concepts of up to a factor of five in the energy storage capacity. This compactness benchmark is a useful design tool to choose a suitable mechanism to realize a compact implementation. More compact ASMs will improve the handling of assistive robots with a physically adjustable stiffness, such as the VariLeg, to support handicapped people in everyday life.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051010-051010-6. doi:10.1115/1.4037565.

In tensegrity robots, the ball tensegrity robot attracts the most attention. The method of driving the ball tensegrity robot is analyzed here. At first, the ball tensegrity structure is described, and its mathematical model is setup. Through analysis, the method for driving bars to make the robot deform and roll is selected. A method for analyzing the deformation of the tensegrity robot is studied. In the method, the nodes are regarded as the objects and displacement increment of the nodes is the product of displacement mode of the robot structure and unbalanced forces on the nodes. The method is applied to analyze deformation of the robot driven by the bars. The methods of driving the robot on two ground-touching triangles are studied. Then, through experiments with the physical model, the methods are verified. A continuous movement of the model is done further to prove the correctness of the analysis. The method for driving bars to make the ball tensegrity robot deform and roll is obtained finally.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051011-051011-8. doi:10.1115/1.4037440.

In this paper, we demonstrate the application of a discrete control Lyapunov function (DCLF) for exponential orbital stabilization of the simplest walking model supplemented with an actuator between the legs. The Lyapunov function is defined as the square of the difference between the actual and nominal velocity of the unactuated stance leg at the midstance position (stance leg is normal to the ramp). The foot placement is controlled to ensure an exponential decay in the Lyapunov function. In essence, DCLF does foot placement control to regulate the midstance walking velocity between successive steps. The DCLF is able to enlarge the basin of attraction by an order of magnitude and to increase the average number of steps to failure by 2 orders of magnitude over passive dynamic walking. We compare DCLF with a one-step dead-beat controller (full correction of disturbance in a single step) and find that both controllers have similar robustness. The one-step dead-beat controller provides the fastest convergence to the limit cycle while using least amount of energy per unit step. However, the one-step dead-beat controller is more sensitive to modeling errors. We also compare the DCLF with an eigenvalue-based controller for the same rate of convergence. Both controllers yield identical robustness but the DCLF is more energy-efficient and requires lower maximum torque. Our results suggest that the DCLF controller with moderate rate of convergence provides good compromise between robustness, energy-efficiency, and sensitivity to modeling errors.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051012-051012-10. doi:10.1115/1.4037566.

This paper presents a framework based on multiport network theory for modeling underactuated grippers where the actuators produce finger motion by deforming an elastic transmission mechanism. If the transmission is synthesized from compliant components joined together with series (equal force) or parallel (equal displacement) connections, the resulting multiport immittance (stiffness) matrix for the entire transmission can be used to deduce how the object will behave in the grasp. To illustrate this, a three-fingered gripper is presented in which each finger is driven by one of two linear two-port spring networks. The multiport approach predicts contact force distribution with good fidelity even with asymmetric objects. The parallel-connected configuration exhibited object rotation and was more prone to object ejection than the series-connected case, which balanced the contact forces evenly.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051013-051013-11. doi:10.1115/1.4037547.

We report some recent advances in kinematics and singularity analysis of the mirror-symmetric N-UU parallel wrists using symmetric space theory. We show that both the finite displacement and infinitesimal singularity kinematics of a N-UU wrist are governed by the mirror symmetry property and half-angle property of the underlying motion manifold, which is a symmetric submanifold of the special Euclidean group SE(3). Our result is stronger than and may be considered a closure of Hunt's argument for instantaneous mirror symmetry in his pioneering exposition of constant velocity shaft couplings. Moreover, we show that the wrist can, to some extent, be treated as a spherical mechanism, even though dependent translation exists, and the singularity-free workspace of a N-UU wrist may be analytically derived. This leads to a straightforward optimal design for maximal singularity-free workspace.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051014-051014-11. doi:10.1115/1.4037617.

The in-pipe robots based on screw drive mechanism are very promising in the aspects of pipe inspecting and maintaining. The novel design of an in-pipe robot with differential screw angles is presented for the curved pipes and vertical straight pipes. The robot is mainly composed of the screw drive mechanism, adaptive linkage mechanism, and the elastic arm mechanism. The alternative adjusting abilities of the mobile velocity and traction, and the adaptive steering ability in curved pipes, are achieved by the special designs. A parameter design approach in consideration of the climbing and steering abilities is proposed in detail for the springs and length of the elastic arms. The results are applied to the prototype design of the robot. In several groups of experiments, the proposed robot is competent to pass through curved pipes and vertical straight pipes. The results prove that the proposed mechanism and parameter design approach are both valid.

Topics: Robots , Screws , Design , Pipes , Springs , Rollers
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051015-051015-13. doi:10.1115/1.4037568.

Two-degree-of-freedom (2DOF) pointing mechanisms, including the gimbal structure, the 1-RR&2-RRR spherical parallel mechanism (SPM), and the Omni-Wrist III, are increasingly applied in tracking devices, mechanical transmission, and artificial joint. Though they share the same number of degree-of-freedom at any given configuration, they will exhibit and transfer different motion characteristics, such as rotation and rolling, when moving continuously. Thanks to the concept of operation mode, these three mechanisms' distinct continuous motion characteristics can be identified and further compared through Euler parameter quaternions, Euler angles, algebraic geometry, and axodes so that the appropriate mechanism for tracking or transmission can be selected. At first, elementary operation modes are numerated based on the number of zero components in a quaternion. In order to acquire all possible operation modes, a set of constraint equations relating to each mechanism are formulated, and an algebraic geometry method is adopted to solve the constraint equations that are much too complicated. For rotation, namely, 1DOF (one-degree-of-freedom) operation mode, its continuous rotation axes are investigated. As to rolling, namely, 2DOF operation mode, allowing for the fact that the difference in 2DOF operation mode of the three mechanisms is not intuitive, axode characteristics of the three mechanisms are investigated and compared. It is found that from the above process of identification and comparison on rotation and rolling, the three mechanisms' distinctive motion characteristics can be effectively obtained.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):051016-051016-10. doi:10.1115/1.4037618.

A hierarchical approach for the lightweight design of a 3-SPR parallel mechanism (PM) is presented in this paper. The criterion to match the rigidities of the limb body and those of the joints is proposed; meanwhile, the constraints in terms of technological processes and the dimensional correlations among components and joints, etc., are considered in this approach. Based on these considerations, the design flow is developed by maximizing the lower-order natural frequencies as well as by minimizing the weights of the limbs/subassemblies subject to specified rigidity constraints attributed to them. The proposed approach simultaneously enables the PM to achieve both high static rigidities and high dynamic behaviors.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Mechanisms Robotics. 2017;9(5):054501-054501-5. doi:10.1115/1.4036740.

Modular robotics is a popular topic for robotic applications and design. The reason behind this popularity is the ability to use and reuse the same robot modules for accomplishing different tasks through reconfiguration. The robots are capable of self-reconfiguration based on the requirements of the task and environmental constraints. It is possible to have a large number of configuration combinations for the same set of modules. Therefore, it is important to identify unique configurations from among the full set of possible configurations and establish a kinematic strategy for each before reconfiguring the robots into a new shape. This becomes more difficult for robot units having more than one connection type and more degrees of freedom (DOF) For example, ModRED II modules have two types of connections and four DOF per module. In this paper, the set of configurations is enumerated, and determination of configuration isomorphism is accomplished for ModRED II modules using graph theory. Kinematic equations are then derived for unique configurations. The kinematic method is then demonstrated for certain example configurations using ModRED II modules.

Topics: Kinematics , Robots
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):054502-054502-12. doi:10.1115/1.4037000.

This paper presents an evolutionary soft-add topology optimization method for synthesis of compliant mechanisms. Unlike the traditional hard-kill or soft-kill approaches, a soft-add scheme is proposed in this study where the elements are equivalent to be numerically added into the analysis domain through the proposed approach. The objective function in this study is to maximize the output displacement of the analyzed compliant mechanism. Three numerical examples are provided to demonstrate the effectiveness of the proposed method. The results show that the optimal topologies of the analyzed compliant mechanisms are in good agreement with previous studies. In addition, the computational time can be greatly reduced by using the proposed soft-add method in the analysis cases. As the target volume fraction in topology optimization for the analyzed compliant mechanism is usually below 30% of the design domain, the traditional methods which remove unnecessary elements from 100% turn into inefficient. The effect of spring stiffness on the optimized topology has also been investigated. It shows that higher stiffness values of the springs can obtain a clearer layout and minimize the one-node hinge problem for two-dimensional cases. The effect of spring stiffness is not significant for the three-dimensional case.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):054503-054503-10. doi:10.1115/1.4037186.

Dynamic characteristics analysis is very important for the design and application of compliant mechanisms, especially for dynamic and control performance in high-speed applications. Although pseudo-rigid-body (PRB) models have been extensively studied for kinetostatic analysis, their accuracy for dynamic analysis is relatively less evaluated. In this paper, we first evaluate the accuracy of the PRB model by comparing against the continuum model using dynamic simulations. We then investigate the effect of mass distribution on dynamics of PRB model for compliant parallel-guided mechanisms. We show that when the beam mass is larger than 10% of the motion stage, the error is significant. We then propose a new PRB model with a corrected mass distribution coefficient which significantly reduces the error of the PRB model. And the dynamic responses are also analyzed according to the corrected mass distribution coefficient. At last, a compliant double parallel-guiding mechanism is used as a case study for validation of the new PRB model for dynamics of compliant mechanisms.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(5):054504-054504-6. doi:10.1115/1.4037548.

Parallel tracking mechanism with varied axes has great potential in actuating antenna to track moving targets. Due to varied rotational axes, its finite motions have not been modeled algebraically. This makes its type synthesis remain a great challenge. Considering these issues, this paper proposes a conformal geometric algebra (CGA) based approach to model its finite motions in an algebraic manner and parametrically generate topological structures of available open-loop limbs. Finite motions of rigid body, articulated joints, and open-loop limbs are formulated by outer product of CGA. Then, finite motions of parallel tracking mechanism with varied axes are modeled algebraically by two independent rotations and four dependent motions with the assistance of kinematic analysis. Afterward, available four degrees-of-freedom (4-DoF) open-loop limbs are generated by using revolute joints to realize dependent motions, and available five degrees-of-freedom (5-DoF) open-loop limbs are obtained by adding one finite rotation to the generated open-loop limbs. Finally, assembly principles in terms of minimal number and combinations of available open-loop limbs are defined. Typical topological structures are synthesized and illustrated.

Commentary by Dr. Valentin Fuster

Errata

J. Mechanisms Robotics. 2017;9(5):057001-057001-1. doi:10.1115/1.4037077.

In Appendix B, Hopper Technical Details, the leaf spring thickness was erroneously stated as 0.045 mm. The correct thickness is 0.45 mm.

Commentary by Dr. Valentin Fuster

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