Research Papers

J. Mechanisms Robotics. 2017;9(3):031001-031001-13. doi:10.1115/1.4035797.

In this work, the kinematics of a large size tunnel digging machine is investigated. The closed-loop mechanism is made by 13 links and 13 class 1 couplings, seven of which are actuated. This kind of machines are commonly used to perform ground drilling for the placement of reinforcement elements during the construction of tunnels. The direct kinematic solution is obtained using three methods: the first two are based on the numerical solution of the closure equation written using the Denavit–Hartenberg convention, while the third is based on the definition and solution in closed form of an equivalent spherical mechanism. The procedures have been tested and implemented with reference to a real commercial tunnel digging machine. The use of the proposed method for the closed-form solution of direct kinematics allows to obtain a major reduction of the computation time in comparison with the standard numerical solution of the closure equation.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031002-031002-8. doi:10.1115/1.4035985.

This paper presents a methodology for synthesizing planar linkages to approximate any prescribed periodic function. The mechanisms selected for this task are the slider-crank and the geared five-bar with connecting rod and sliding output (GFBS), where any number of double-crank (or drag-link) four-bars are used as drivers. A slider-crank mechanism, when comparing the input crank rotation to the output slider displacement, produces a sinusoid-like function. Instead of directly driving the input crank, a drag-link four-bar may be added to drive the crank from its output via a rigid connection between the two. Driving the input of the added four-bar results in a function that modifies the sinusoid-like curve. This process can be continued through the addition of more drag-link mechanisms to the device, progressively altering the curve toward any periodic function with a single maximum. For periodic functions with multiple maxima, a GFBS is used as the terminal linkage added to the chain of drag-link mechanisms. The synthesis process starts by analyzing one period of the function to design either the terminal slider-crank or terminal GFBS. matlab's fmincon command is then utilized as the four-bars are added to reduce the structural error between the desired function and the input–output function of the mechanism. Mechanisms have been synthesized in this fashion to include a large number of links that are capable of closely producing functions with a variety of intriguing features.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031003-031003-13. doi:10.1115/1.4035798.

This paper presents a general algorithm for solving the dynamic of tree structure robots with rigid and flexible links, active and passive joints, and with a fixed or floating base. The algorithm encompasses in a unified approach both the inverse and direct dynamics. It addresses also the hybrid case where each active joint is considered with known joint torque as in the direct dynamic case, or with known joint acceleration as in the inverse dynamic case. To achieve this goal, we propose an efficient recursive approach based on the generalized Newton–Euler equations of flexible tree-structure systems. This new general hybrid algorithm is easy to program either numerically or using efficient customized symbolic techniques. It is of great interest for studying floating base systems with soft appendages as those currently investigated in soft bio-inspired robotics or when a robotic system has to modify its structure for some particular tasks, such as transforming an active joint into a compliant flexible one, or modifying a task with a floating base into one with fixed base.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031004-031004-11. doi:10.1115/1.4035681.

Adaptive cable-driven parallel robots are a special subclass of cable-driven systems in which the locations of the pulley blocks are modified as a function of the end-effector pose to obtain optimal values of given performance indices within a target workspace. Due to their augmented kinematic redundancy, such systems enable larger workspace volume and higher performance compared to traditional designs featuring the same number of cables. Previous studies have introduced a systematic method to optimize design and trajectory planning of the moving pulley-blocks for a given performance index. In this paper, we study the motions of the pulley blocks that optimize two performance indices simultaneously: stiffness and dexterity. Specifically, we present a method to determine the pulley blocks motions that guarantee ideal dexterity with the best feasible elastic stiffness, as well as those that guarantee isotropic elastic stiffness with the best feasible dexterity. We demonstrate the proposed approach on some practical cases of planar adaptive cable-driven parallel robots.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031005-031005-8. doi:10.1115/1.4035986.

The pseudo-rigid-body model (PRBM) used to simulate compliant beams without inflection point had been well developed. In this paper, two types of PRBMs are proposed to simulate the large deflection of flexible beam with an inflection point in different configurations. These models are composed of five rigid links connected by three joints added with torsional springs and one hinge without spring representing the inflection point in the flexural beam. The characteristic radius factors of the PRBMs are determined by solving the objective function established according to the relative angular displacement of the two rigid links jointed by the hinge via genetic algorithm. The spring stiffness coefficients are obtained using a linear regression technique. The effective ranges of these two models are determined by the load index. The numerical result shows that both the tip locus and inflection point of the flexural beam with single inflection can be precisely simulated using the model proposed in this paper.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031006-031006-10. doi:10.1115/1.4035990.

Radiotherapy (RT) enables a selective destruction of tumor cells, although the treatment area is limited to the irradiated volume. Any RT technique comes along with multiple sources of error, which can lead to a deviation of the dose that is applied to the patient. Phantoms—structures that replicate a human and include measurement technology to assess the applied dosage—are used to make such errors observable. Past RT-technologies assumed static tumors. Correspondingly, most existing phantoms comprise only static components. Nowadays, RT is at a transition stage toward techniques which explicitly account for physiological motion. These techniques require phantoms generating such motion. Consequentially, a demand for new kinds of manipulators, which operate with a RT-phantom, has come up and will further increase in the future. Key demands of such manipulators are among others, the generation of full rigid body motion, high acceleration, high stiffness, compactness, little weight, and easy portability. Another indispensable feature is the spatial separation of mechatronic components and phantom structure to ensure human equivalency of the latter. In this work, a new kind of parallel kinematic manipulator (PKM), which is tailored to the requirements of RT-phantom technology, is presented. The PKM consists of low cost standardized mechanical components and sets the target structures, which are located inside a human-equivalent area, into translational and rotational motion in three degrees-of-freedom (DOFs). Only a part of the end-effector is located within the human-equivalent area. All the remaining parts of the PKM are located outside that area. Two versions of the manipulator are presented in detail: their kinematics are derived and their kinetostatic properties are compared. This includes a workspace analysis and the analysis of the transmission behavior in general, meaning the influence of the most important design parameters on the performance. It can be shown that practical differences of both kinematics are negligible, while the modified version provides significant mechanical advantages. In conclusion, a first special purpose manipulator for application in the evolving field of RT-phantom technology is presented. The PKM, which employs a novel kinematic structure, provides higher suitability for its purpose than any other robotic system employed so far for the same purpose.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031007-031007-10. doi:10.1115/1.4035542.

In this paper, we examine two spherical parallel manipulators (SPMs) constructed with legs that include planar and spherical subchains that combine to impose constraints equivalent to hidden revolute joints. The first has supporting serial chain legs constructed from three revolute joints with parallel axes, denoted RRR, followed by two revolute joints that have intersecting axes, denoted RR̂. The leg has five degrees-of-freedom and is denoted RRR-RR̂. Three of these legs can be assembled so the spherical chains all share the same point of intersection to obtain a spherical parallel manipulator denoted as 3-RRR-RR̂. The second spherical parallel manipulator has legs constructed from three revolute joints that share one point of intersection, denoted RRR̂, and a second pair of revolute joints with axes that intersect in a different point. This five-degree-of-freedom leg is denoted RRR̂-RR̂. The spherical parallel manipulator constructed from these legs is 3-RRR̂-RR̂. We show that the internal constraints of these two types of legs combine to create hidden revolute joints that can be used to analyze the kinematics and singularities of these spherical parallel manipulators. A quaternion formulation provides equations for the quartic singularity varieties some of which decompose into pairs of quadric surfaces which we use to classify these spherical parallel manipulators.

Topics: Manipulators , Chain
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031008-031008-17. doi:10.1115/1.4035682.

Kinematic chains are obtained from the helicoid–helicoid intersections applying the method of surfaces generated by kinematic dyads. Some local properties of the helicoids are used to obtain the bifurcation points in the configuration space of the obtained kinematic chains. It is proven that certain relationships between the two helicoids lead to a periodic behavior of these bifurcations, which suggest that, if the kinematic pairs (P and H) could move without a limit, the kinematic chain would theoretically feature an infinity of operation modes. Finally, a mechanism which is able to change the helicoid–helicoid intersection curve during its motion is proven to change its finite mobility in one of its operation modes.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031009-031009-7. doi:10.1115/1.4035881.

Recently, there has been an increased interest in origami art from a mechanism design perspective. The deployable nature and the planar fabrication method inherent to origami provide potential for space and cost-efficient mechanisms. In this paper, a novel type of origami mechanisms is proposed in which the compliance of the facets is used to incorporate the spring behavior: compliant facet origami mechanisms (COFOMs). A simple model that computes the moment characteristic of a single vertex COFOM has been proposed, using a semispatial version of the pseudo-rigid-body (PRB) theory to model bending of the facets. The PRB model has been evaluated numerically and experimentally, showing good performance. The PRB model is a potential starting point for a design tool which would provide an intuitive way of designing this type of mechanisms including their spring behavior, with very low computational cost.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031010-031010-10. doi:10.1115/1.4035373.

This paper studies the collision problem of a robot manipulator and presents a method to minimize the impact force by pre-impact configuration designing. First, a general dynamic model of a robot manipulator capturing a target is established by spatial operator algebra (SOA) and a simple analytical formula of the impact force is obtained. Compared with former models proposed in literatures, this model has simpler form, wider range of applications, O(n) computation complexity, and the system Jacobian matrix can be provided as a production of the configuration matrix and the joint matrix. Second, this work utilizes the impulse ellipsoid to analyze the influence of the pre-impact configuration and the impact direction on the impact force. To illustrate the inertia message of each body in the joint space, a new concept of inertia quasi-ellipsoid (IQE) is introduced. We find that the impulse ellipsoid is constituted of the inertia ellipsoids of the robot manipulator and the target, while each inertia ellipsoid is composed of a series of inertia quasi-ellipsoids. When all inertia quasi-ellipsoids exhibit maximum (minimum) coupling, the impulse ellipsoid should be the flattest (roundest). Finally, this paper provides the analytical expression of the impulse ellipsoid, and the eigenvalues and eigenvectors are used as measurements to illustrate the size and direction of the impulse ellipsoid. With this measurement, the desired pre-impact configuration and the impact direction with minimum impact force can be easily solved. The validity and efficiency of this method are verified by a PUMA robot and a spatial robot.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031011-031011-16. doi:10.1115/1.4035988.

Cable-driven parallel manipulators (CDPM) potentially offer many advantages over serial manipulators, including greater structural rigidity, greater accuracy, and higher payload-to-weight ratios. However, CDPMs possess limited moment resisting/exerting capabilities and relatively small orientation workspaces. Various methods have been contemplated for overcoming these limitations, each with its own advantages and disadvantages. The focus of this paper is on one such method: the addition of base mobility to the system. Such base mobility gives rise to kinematic redundancy, which needs to be resolved carefully in order to control the system. However, this redundancy can also be exploited in order to optimize some secondary criteria, e.g., maximizing the size and quality of the wrench-closure workspace with the addition of base mobility. In this work, the quality of the wrench-closure workspace is examined using a tension-factor index. Two planar mobile base configurations are investigated, and their results are compared with a traditional fixed-base system. In the rectangular configuration, each base is constrained to move along its own linear rail, with each rail forming right angles with the two adjacent rails. In the circular configuration, the bases are constrained to move along one circular rail. While a rectangular configuration enhances the size and quality of the orientation workspace in a particular rotational direction, the circular configuration allows for the platform to obtain any position and orientation within the boundary of the base circle. Furthermore, if the bases are configured in such a way that the cables are fully symmetric with respect to the platform, a maximum possible tension-factor of one is guaranteed. This fully symmetric configuration is shown to offer a variety of additional advantages: it eliminates the need to perform computationally expensive nonlinear optimization by providing a closed-form solution to the inverse kinematics problem, and it results in a convergence between kinematic singularities and wrench-closure singularities of the system. Finally, we discuss a particular limitation of this fully symmetric configuration: the inability of the cables to obtain an even tension distribution in a loaded configuration. For this reason, it may be useful to relax the fully symmetric cable requirement in order to yield reasonable tensions of equal magnitude.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031012-031012-9. doi:10.1115/1.4035989.

Remote center-of-motion (RCM) parallel manipulators (PMs) are fit for robotized minimally invasive surgery (MIS). RCM PMs with fixed linear actuators have the advantages of high stiffness, reduced moving mass, and higher rigidity and load capacity. However, there are very few available architectures of these types of PMs. Using the Lie group algebraic properties of the set of rigid-body displacements, this paper proposes a new family of RCM PMs with fixed linear actuators for MIS. The general motion with a remote center has four degrees-of-freedom (DOF) and is produced by the in-series concatenation of a spherical S pair and a prismatic P pair and, therefore, is said to be SP equivalent. The SP-equivalent PMs can be used in minimally invasive surgery. First, the kinematic bonds of limb chains and their mechanical generators for SP-equivalent RCM PMs are presented. Limb chains with fixed linear actuators are then derived using the closure of products in subgroups. Structural conditions for constructing an SP-equivalent RCM PM with linear fixed actuators are revealed. Helical pairs are introduced to remove a local rotation and yield a 360-deg-rotation capability of the moving platform. Numerous new architectures with practical potential are presented.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031013-031013-9. doi:10.1115/1.4035991.

Minimally invasive surgery (MIS) requires four degrees-of-freedom (DOFs) (pitch, translation, yaw, and roll) at the incision point, but the widely used planar remote center of motion (RCM) mechanisms only provide one degree-of-freedom. The remaining three DOFs are achieved through external means (such as cable-pulleys or actuators mounted directly on the distal-end) which adversely affect the performance and design complexity of a surgical manipulator. This paper presents a new RCM mechanism which provides the two most important DOFs (pitch and translation) by virtue of its mechanical design. Kinematics of the new mechanism is developed and its singularities are analyzed. To achieve maximum performance in the desired workspace region, an optimal configuration is also evaluated. The design is optimized to yield maximum manipulability and tool translation with smallest size of the mechanism. Unlike the traditional planar RCM mechanisms, the proposed design does not rely on external means to achieve translation DOF, and therefore, offers potential advantages. The mechanism can be a suitable choice for surgical applications demanding a compact distal-end or requiring multiple manipulators to operate in close proximity.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031014-031014-10. doi:10.1115/1.4035802.

This paper presents a novel passive redundant spherical joint with a very large range of motion. A kinematic model is first developed in order to provide a framework for the analysis. The principle of the redundant joint is then introduced. The proposed joint does not require any active component since the redundancy is passively handled using springs. A static model of the joint is developed in order to clearly demonstrate how all singularities or jamming configurations can be avoided. Two possible arrangements are presented, one using linear springs and one using a torsional spring. Finally, experimental prototypes are demonstrated that can attain a range of tilt angle of ±150 deg.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031015-031015-5. doi:10.1115/1.4035532.

A configuration of a mechanical linkage is defined as regular if there exists a subset of actuators with their corresponding Jacobian columns spans the gripper's velocity space. All other configurations are defined in the literature as singular configurations. Consider mechanisms with grippers' velocity space m. We focus our attention on the case where m Jacobian columns of such mechanism span m, while all the rest are linearly dependent. These are obviously an undesirable configuration, although formally they are defined as regular. We define an optimal-regular configuration as such that any subset of m actuators spans an m-dimensional velocity space. Since this densely constraints the work space, a more relaxed definition is needed. We therefore introduce the notion of k-singularity of a redundant mechanism which means that rigidifying k actuators will result in an optimal-regularity. We introduce an efficient algorithm to detect a k-singularity, give some examples for cases where m = 2, 3, and demonstrate our algorithm efficiency.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031016-031016-12. doi:10.1115/1.4035987.

Torque control of small-scale robotic devices such as hand exoskeletons is challenging due to the unavailability of miniature and compact bidirectional torque actuators. In this work, we present a miniature Bowden-cable-based series elastic actuator (SEA) using helical torsion springs. The three-dimensional (3D) printed SEA is 38 mm × 38 mm × 24 mm in dimension and weighs 30 g, excluding motor which is located remotely. We carry out a thorough experimental testing of our previously presented linear compression spring SEA (LC-SEA) (Agarwal et al. 2015, “An Index Finger Exoskeleton With Series Elastic Actuation for Rehabilitation: Design, Control and Performance Characterization,” Int. J. Rob. Res., 34(14), pp. 1747–1772) and helical torsion spring SEA (HT-SEA) and compare the performance of the two designs. Performance characterization on a test rig shows that the two SEAs have adequate torque source quality (RMSE < 12% of peak torque) with high torque fidelities (>97% at 0.5 Hz torque sinusoid) and force tracking bandwidths of 2.5 Hz and 4.5 Hz (0.2 N·m), respectively, which make these SEAs suitable for our application of a hand exoskeleton.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031017-031017-13. doi:10.1115/1.4035800.

In recent years, applications in industrial assemblies within a size range from 0.5 mm to 100 mm are increasing due to the large demands for new products, especially those associated with digital multimedia. Research on grippers or robotic hands within the mesoscopic scale of this range has not been explored in any great detail. This paper outlines the development of a gripper to bridge the gap between microgrippers and macrogrippers by extending the gripping range to the mesoscopic scale, particularly without the need to switch grippers during industrial assembly. The mesoscopic scale gripper (meso-gripper) researched in this work has two modes of operation: passive adjusting mode and angled gripping mode, adapting its configuration to the shape of object automatically. This form of gripping and the associated mechanism are both novel in their implementation and operation. First, the concept of mesoscopic scale in robotic gripping is presented and contextualized around the background of inefficient hand switching processes and applications for assembly. The passive adjusting and angled gripping modes are then analyzed and a dual functional mechanism design proposed. A geometric constraint method is then demonstrated which facilitates task-based dimensional synthesis after which the kinematics of synthesized mechanism is investigated. The modified synthesized mechanism gripper is then investigated according to stiffness and layout. Finally, a 3D printed prototype is successfully tested, and the two integrated gripping modes for universal gripping verified.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(3):031018-031018-12. doi:10.1115/1.4035993.

This paper introduces a general method for analyzing flexure systems of any configuration, including those that cannot be broken into parallel and serial subsystems. Such flexure systems are called interconnected hybrid flexure systems because they possess limbs with intermediate bodies that are connected by flexure systems or elements. Specifically, the method introduced utilizes screw algebra and graph theory to help designers determine the freedom spaces (i.e., the geometric shapes that represent all the ways a body is permitted to move) for all the bodies joined together by compliant flexure elements within interconnected hybrid flexure systems (i.e., perform mobility analysis of general flexure systems). This method also allows designers to determine (i) whether such systems are under-constrained or not and (ii) whether such systems are over-constrained or exactly constrained (i.e., perform constraint analysis of general flexure systems). Although many flexure-based precision motion stages, compliant mechanisms, and microarchitectured materials possess topologies that are highly interconnected, the theory for performing the mobility and constraint analysis of such interconnected flexure systems using traditional screw theory does not currently exist. The theory introduced here lays the foundation for an automated tool that can rapidly generate the freedom spaces of every rigid body within a general flexure system without having to perform traditional computationally expensive finite element analysis. Case studies are provided to demonstrate the utility of the proposed theory.

Commentary by Dr. Valentin Fuster

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