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Research Papers

J. Mechanisms Robotics. 2018;10(3):031001-031001-9. doi:10.1115/1.4038218.

The kinematic chains that generate the planar motion group in which the prismatic-joint direction is always perpendicular to the revolute-joint axis have shown their effectiveness in type synthesis and mechanism analysis in parallel mechanisms. This paper extends the standard prismatic–revolute–prismatic (PRP) kinematic chain generating the planar motion group to a relatively generic case, in which one of the prismatic joint-directions is not necessarily perpendicular to the revolute-joint axis, leading to the discovery of a pseudo-helical motion with a variable pitch in a kinematic chain. The displacement of such a PRP chain generates a submanifold of the Schoenflies motion subgroup. This paper investigates for the first time this type of motion that is the variable-pitched pseudo-planar motion described by the above submanifold. Following the extraction of a helical motion from this skewed PRP kinematic chain, this paper investigates the bifurcated motion in a 3-prismatic–universal–prismatic (PUP) parallel mechanism by changing the active geometrical constraint in its configuration space. The method used in this contribution simplifies the analysis of such a parallel mechanism without resorting to an in-depth geometrical analysis and screw theory. Further, a parallel platform which can generate this skewed PRP type of motion is presented. An experimental test setup is based on a three-dimensional (3D) printed prototype of the 3-PUP parallel mechanism to detect the variable-pitched translation of the helical motion.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031002-031002-12. doi:10.1115/1.4039002.

This paper for the first time reveals a set of special plane-symmetric Bricard linkages with various branches of reconfiguration by means of intersection of two generating toroids, and presents a complete theory of the branch reconfiguration of the Bricard plane-symmetric linkages. An analysis of the intersection of these two toroids reveals the presence of coincident conical singularities, which lead to design of the plane-symmetric linkages that evolve to spherical 4R linkages. By examining the tangents to the curves of intersection at the conical singularities, it is found that the linkage can be reconfigured between the two possible branches of spherical 4R motion without disassembling it and without requiring the usual special configuration connecting the branches. The study of tangent intersections between concentric singular toroids also reveals the presence of isolated points in the intersection, which suggests that some linkages satisfying the Bricard plane-symmetry conditions are actually structures with zero finite degrees-of-freedom (DOF) but with higher instantaneous mobility. This paper is the second part of a paper published in parallel by the authors in which the method is applied to the line-symmetric case.

Topics: Linkages
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031003-031003-11. doi:10.1115/1.4038981.

This paper for the first time investigates a family of line-symmetric Bricard linkages by means of two generated toroids and reveals their intersection that leads to a set of special Bricard linkages with various branches of reconfiguration. The discovery is made in the concentric toroid–toroid intersection. By manipulating the construction parameters of the toroids, all possible bifurcation points are explored. This leads to the common bi-tangent planes that present singularities in the intersection set. The study reveals the presence of Villarceau and secondary circles in the toroid–toroid intersection. Therefore, a way to reconfigure the Bricard linkage to a pair of different types of Bennett linkage is uncovered. Further, a linkage with two Bricard and two Bennett motion branches is explored. In addition, the paper reveals the Altmann linkage as a member of the family of special line-symmetric Bricard linkage studied in this paper. The method is applied to the plane-symmetric case in the following paper published together with this paper.

Topics: Linkages
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031004-031004-10. doi:10.1115/1.4039499.

Cable-suspended robots may move beyond their static workspace by keeping all cables under tension, thanks to end-effector inertia forces. This may be used to extend the robot capabilities, by choosing suitable dynamical trajectories. In this paper, we consider three-dimensional (3D) elliptical trajectories of a point-mass end effector suspended by three cables from a base of generic geometry. Elliptical trajectories are the most general type of spatial sinusoidal motions. We find a range of admissible frequencies for which said trajectories are feasible; we also show that there is a special frequency, which allows the robot to have arbitrarily large oscillations. The feasibility of these trajectories is verified via algebraic conditions that can be quickly verified, thus being compatible with real-time applications. By generalizing previous studies, we also study the possibility to change the frequency of oscillation: this allows the velocity at which a given ellipse is tracked to be varied, thus providing more latitude in the trajectory definition. We finally study transition trajectories to move the robot from an initial state of rest (within the static workspace) to the elliptical trajectory (and vice versa) or to connect two identical ellipses having different centers.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031005-031005-12. doi:10.1115/1.4039498.

This paper presents the design of a multimode compliant gripper, using the singularities of the four-bar mechanism with equilateral links. The mobility of the compliant gripper can be reconfigurable to grasp a variety of shapes or adapt to specific requirements. The compliant gripper is a compact and two-layer structure. Two linear actuators are required to enable the multiple operation modes, by the conversion of two pairs of slider-crank mechanisms. A multimode compliant four-bar mechanism is first presented and kinematically analyzed. The design and the kinetostatic modeling of the resulting compliant gripper are then performed. Finally, the analysis of the reconfigurable compliant gripper under different actuation schemes is carried out, including the comparison of the results obtained from analytical modeling, finite element analysis (FEA), and experimental testing.

Topics: Design , Grippers
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031006-031006-12. doi:10.1115/1.4039065.

Compliant universal joints have been widely employed in high-precision fields due to plenty of good performance. However, the stiffness characteristics, as the most important consideration for compliant mechanisms, are rarely involved. In this paper, a deterministic design for a constraint-based compliant parallel universal joint with constant rotational stiffness is presented. First, a constant stiffness realization principle is proposed by combination of the freedom and constraint topology (FACT) method and beam constraint model (BCM) to establish a mapping relationship between stiffness characteristics and topology configurations. A parallel universal joint topology is generated by the constant stiffness realization principle. Then, the analytical stiffness model of the universal joint with some permissible approximations is formulated based on the BCM, and geometrical prerequisites are derived to achieve the desired constant rotational stiffness. After that, finite element analysis (FEA), experimental testing, and detailed stiffness analysis are carried out. It turns out that the rotational stiffness of the universal joint can keep constant with arbitrary azimuth angles even if the rotational angle reaches up to ±5 deg. Meanwhile, the acceptable relative errors of rotational stiffness are within 0.53% compared with the FEA results and 2.6% compared with the experimental results, which indicates the accuracy of the theoretical stiffness model and further implies the feasibility of constant stiffness realization principle on guiding the universal joint design.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031007-031007-8. doi:10.1115/1.4039222.

An estimated 230,000 above-knee amputees in India are currently in need of prosthetic devices, a majority of them facing severe socio-economic constraints. However, only a few passive prosthetic knee devices in the market have been designed for facilitation of normative gait kinematics and for meeting the specific daily life needs of above-knee amputees in the developing world. Based on the results of our past studies, this paper establishes a framework for designing a potentially low-cost, fully passive prosthetic knee device, which aims to facilitate able-bodied kinematics at a low metabolic cost. Based on a comprehensive set of functional requirements and biomechanical analysis from our past work, we present an early prototype mechanism for the prosthetic knee joint that is primarily focused on enabling able-bodied kinematics. The mechanism is implemented using two functional modules: an automatic early stance lock for stability and a differential friction damping system for late stance and swing control. For preliminary, qualitative validation of the knee mechanism, we carried out a field trial on four above-knee amputees in India, which showed satisfactory performance of the early stance lock. The prototype enabled smooth stance-to-swing transition by timely initiation of late stance flexion. Possible methods of incorporating an additional spring module for further refinement of the design are also discussed, which can enable flexion-extension during the early-stance phase of the gait cycle and potentially reduce the metabolic energy expenditure of the user further.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031008-031008-11. doi:10.1115/1.4039496.

In this paper, we examine the question of whether parallel elastic actuation or series elastic actuation is better suited for hopping robots. To this end, we compare and contrast the two actuation concepts in energy optimal hopping motions. To enable a fair comparison, we employ optimal control to identify motion trajectories, actuator inputs, and system parameters that are optimally suited for each actuator concept. In other words, we compare the best possible hopper with parallel elastic actuation to the best possible hopper with series elastic actuation. The optimizations are conducted for three different cost functions: positive mechanical motor work, thermal electrical losses, and positive electrical work. Furthermore, we look at three representative cases for converting rotary motor motion to linear leg motion in a legged robot. Our model featured an electric DC-motor model, a gearbox with friction, damping in the leg spring, and contact collisions. We find that the optimal actuator choice depends both on the cost function and conversion of motor motion to leg motion. When considering only thermal electrical losses, parallel elastic actuation always performs better. In terms of positive mechanical motor work and positive electrical work, series elastic actuation is better when there is little friction in the gear-train. For higher gear-train friction parallel elastic actuation is more economical for these cost functions as well.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031009-031009-13. doi:10.1115/1.4039394.

This paper presents unified control schemes for compliant humanoid robots that are aimed at ensuring successful execution of both balancing tasks and walking trajectories for this class of bipeds, given the complexity of under-actuation. A set of controllers corresponding to the single-support (SS) and double-support (DS) walking phases has been designed based on the flexible sagittal joint dynamics of the system, accounting for both the motor and link states. The first controller uses partial state feedback (proportional–derivative–derivative (PDD)), whereas the second considers the full state of the robot (proportional–proportional–derivative–derivative (PPDD)), while both are mathematically proven to stabilize the closed-loop systems for regulation and trajectory tracking tasks. It is demonstrated mathematically that the PDD controller possesses better stability properties than the PPDD scheme for regulation tasks, even though the latter has the advantage of allowing for its associated gain-set to be generated by means of standard techniques, such as linear quadratic regulator (LQR) control. A switching condition relating the center-of-pressure (CoP) to the energy functions corresponding to the DS and SS models has also been established. The theoretical results are corroborated by means of balancing and walking experiments using the COmpliant huMANoid (COMAN), while a practical comparison between the designed controller and a classical PD controller for compliant robots has also been performed. Overall, and a key conclusion of this paper, the PPDD scheme has produced a significantly improved trajectory tracking performance, with 9%, 15%, and 20% lower joint space error for the hip, knee, and ankle, respectively.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031010-031010-10. doi:10.1115/1.4039395.

Real-time motion planning of robots in a dynamic environment requires a continuous evaluation of the determined trajectory so as to avoid moving obstacles. This is even more challenging when the robot also needs to perform a task optimally while avoiding the obstacles due to the limited time available for generating a new collision-free path. In this paper, we propose the sequential expanded Lagrangian homotopy (SELH) approach, which is capable of determining the globally optimal robot's motion sequentially while satisfying the task constraints. Through numerical simulations, we demonstrate the capabilities of the approach by planning an optimal motion of a redundant mobile manipulator performing a complex trajectory. Comparison against existing optimal motion planning approaches, such as genetic algorithm (GA) and neural network (NN), shows that SELH is able to perform the planning at a faster rate. The considerably short computational time opens up an opportunity to apply this method in real time; and since the robot's motion is planned sequentially, it can also be adjusted to accommodate for dynamically changing constraints such as moving obstacles.

Topics: Robots , Path planning
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031011-031011-8. doi:10.1115/1.4039396.

Remote center of motion (RCM) mechanisms are often used in surgical robots for laparoscopic surgery. In this paper, a RCM mechanism for holding a robotic forceps that facilitates adjustment using a flexible structure is proposed. The flexible structure is designed and manufactured with polypropylene-like resin material using a three-dimensional (3D) printer. Super elastic NI-Ti rods are inserted in the structure to have elasticity for bending and have rigidity for twisting. The structure achieves pitch motion around the remote center with two pneumatic cylinders. One cylinder drives the position and the other cylinder controls the bending radius of the structure. Therefore, the location of the remote center can be variable. This allows easier adjustment of the remote center before or during operation. The holder robot including the mechanism has four degrees-of-freedom (DOFs) in total, consisting of the pitch, a rotation around yaw axis, a translation in the direction of forceps insertion and a rotation of the forceps. Pneumatic rotary actuators are used for rotations and a cylinder is used for the translational motion. The model of the flexible structure is derived experimentally to design a controller for the pitch motion. A pneumatically driven robotic forceps is mounted on the holder to construct a master–slave control system. Experimental results show that the proposed control law achieves the desired rotational pitch motion. We compare the holder with a rigid link RCM holder and confirm the robustness of the proposed holder for variable remote center. Finally, the effectiveness of the system is confirmed with suturing tasks using a phantom tissue.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031012-031012-10. doi:10.1115/1.4039223.

This paper presents a general discretization-based approach to the large deflection problems of spatial flexible links in compliant mechanisms. Based on the principal axes decomposition of structural compliance matrices, a particular type of elements, which relate to spatial six degrees-of-freedom (DOF) serial mechanisms with passive elastic joints, is developed to characterize the force-deflection behavior of the discretized small segments. Hence, the large deflection problems of spatial flexible rods can be transformed to the determination of static equilibrium configurations of their equivalent hyper-redundant mechanisms. The main advantage of the proposed method comes from the use of robot kinematics/statics, rather than structural mechanics. Thus, a closed-form solution to the system overall stiffness can be derived straightforwardly for efficient gradient-based searching algorithms. Two kinds of typical equilibrium problems are intensively discussed and the correctness has been verified by means of physical experiments. In addition, a 2DOF planar compliant parallel manipulator is provided as a case study to demonstrate the potential applications.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031013-031013-10. doi:10.1115/1.4039224.

This paper deals with a 6R single-loop overconstrained spatial mechanism that has two pairs of revolute joints with intersecting axes and one pair of revolute joints with parallel axes. The 6R mechanism is first constructed from an isosceles triangle and a pair of identical circles. The kinematic analysis of the 6R mechanism is then dealt with using a dual quaternion approach. The analysis shows that the 6R mechanism usually has two solutions to the kinematic analysis for a given input and may have two circuits (closure modes or branches) with one or two pairs of full-turn revolute joints. In two configurations in each circuit of the 6R mechanism, the axes of four revolute joints are coplanar, and the axes of the other two revolute joints are perpendicular to the plane defined by the above four revolute joints. Considering that from one configuration of the 6R mechanism, one can obtain another configuration of the mechanism by simply renumbering the joints, the concept of two-faced mechanism is introduced. The formulas for the analysis of plane symmetric spatial triangle are also presented in this paper. These formulas will be useful for the design and analysis of multiloop overconstrained mechanisms involving plane symmetric spatial RRR triads.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):031014-031014-7. doi:10.1115/1.4039772.

Comparatively slow growth in energy density of both power storage and generation technologies has placed added emphasis on the need for energy-efficient designs in legged robots. This paper explores the potential of parallel springs in robot limb design. We start by adding what we call the exhaustive parallel compliance matrix (EPCM) to the design. The EPCM is a set of parallel springs, which includes a parallel spring for each joint and a multijoint parallel spring for all possible combinations of the robot's joints. Then, we carefully formulate and compare two performance metrics, which improve various aspects of the system performance. Each performance metric is analyzed and compared, their strengths and weaknesses being rigorously presented. The performance benefits associated with this approach are dramatic. Implementing the spring matrix reduces the sum of square power (SSP) exerted by the actuators by up to 47%, the peak power requirement by almost 40%, the sum of squared current by 55%, and the peak current by 55%. These results were generated using a planar robot limb and a gait trajectory borrowed from biology. We use a fully dynamic model of the robotic system including inertial effects. We also test the design robustness using a perturbation study, which shows that the parallel springs are effective even in the presence of trajectory perturbation.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Mechanisms Robotics. 2018;10(3):034501-034501-8. doi:10.1115/1.4039218.

The theory of screws plays a fundamental role in the field of mechanisms and robotics. Based on the rank-one decomposition of positive semidefinite (PSD) matrices, this paper presents a new algorithm to identify the canonical basis of high-order screw systems. Using the proposed approach, a screw system can be decomposed into the direct sum of two subsystems, which are referred to as the general and special subsystems, respectively. By a particular choice of the general subsystem, the canonical basis of the original system can be obtained by the direct combination of the subsystems' principal elements. In the proposed decomposition, not only the canonical form of the screw system but also the corresponding distribution of all those possible base elements can be determined in a straightforward manner.

Topics: Screws
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2018;10(3):034502-034502-8. doi:10.1115/1.4039497.

In this paper, the nonperiodic function synthesis of an RCCC mechanism is presented using a wavelet feature parameter (WFP) method. The output function and the sliding displacement of the RCCC mechanism are described by the wavelet approximate and wavelet details. Based on the relationship of wavelet details of the sliding displacement and its scaling, a normalization method for wavelet details of the sliding displacement is presented. The influence of proportional scaling of the linkage lengths is eliminated. An adaptive database is established. The problem of nonperiodic design requirements of RCCC mechanism function synthesis is solved. To demonstrate the feasibility of this method, two numerical examples are proposed. Based on the nonperiodic design requirements, the RCCC mechanisms are designed and simulated using matlab and catia software. The results show that the method proposed is effective for nonperiodic function generation of the RCCC mechanism with multiple positions.

Commentary by Dr. Valentin Fuster

Design Innovation Paper

J. Mechanisms Robotics. 2018;10(3):035001-035001-12. doi:10.1115/1.4039400.

Most multimode parallel robots can change operation modes by passing through constraint singularities. This paper deals with a comprehensive kinematic study of a three degrees-of-freedom (DOF) multimode three-PRPiR parallel robot developed at Heriot-watt University. This robot is able to reach several operation modes without crossing any constraint singularity by using lockable Pi and R joints. Here, a Pi joint may act as a 1DOF planar parallelogram if its lockable P (prismatic) joint is locked or a 2DOF RR serial chain if its lockable P joint is released. The operation modes of the robot include a 3T operation mode and four 2T1R operation modes with two different directions of the rotation axis of the moving platform. The inverse kinematics and forward kinematics of the robot in each operation mode are dealt with in detail. The joint space and workspace analysis of the robot allow us to know the regions of the workspace that the robot can reach in each operation mode. It is shown that the robot is able to change assembly mode in one operation mode by passing through another operation mode.

Topics: Kinematics , Robots
Commentary by Dr. Valentin Fuster

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