Convex combination of points is a fundamental operation in computational geometry. By considering rigid-body displacements as points in the image spaces of planar quaternions, quaternions and dual quaternions, respectively, the notion of convexity in Euclidean three-space has been extended to kinematic convexity in , and in the context of computational kinematic geometry. This paper deals with computational kinematic geometry of bounded planar objects rather than that of infinitely large moving spaces. In this paper, we present a new formulation for kinematic convexity based on an average-distance minimizing motion sweep of a bounded planar object. The resulting 1-DOF motion sweep between two planar poses is represented as a convex combination in the configuration space defined by where is associated with the location of the centroid of the planar object and with being the angle of rotation. For three poses, a 2-DOF motion sweep is developed that not only minimizes the combined average squared distances but also attains a convex-combination representation so that existing algorithms for convex hull of points can be readily applied to the construction and analysis of kinematic convex hulls. This results in a new type of convex hull for planar kinematics such that its boundaries are defined by the average-distance minimizing sweeps of the bounded planar object.

This article presents an exploratory study of a new family of parallel mechanisms with multiscale (micro/macro) motion capabilities. These composite serial-in-parallel mechanisms use kinematic redundancy and two sets of macro and micro actuators to achieve multiscale motion. Use of twisted wire actuators (TWAs) is considered as a low-cost alternative for achieving micromotion. A kinematically redundant 3RRPR planar parallel robot is used as a case study for task-based design of these robots with considerations of macro and micromotion workspace, dexterity, minimal motion resolution, and end-effector error considering the use of low-cost TWAs for achieving micromotion. Task-based considerations for the microworkspace are used to illustrate the effect of the TWAs on the micromotion kinematics. An experimental study shows that, because of the use of TWAs, it is possible to achieve motion resolutions on the order of a few micrometers despite using low-cost manufacturing techniques and actuators. The use of TWAs is shown to also significantly alter the kinematic characteristics of the robot at the microscale. The modeling framework of this article can guide designers in key design considerations for parallel robots with multiscale motion capabilities. Results of this article can be used to guide users in the selection of TWAs and in determining the threshold when the robot should switch from macro to micromotion and to facilitate a smooth transition via redundancy resolution.

Understanding legged locomotion in various environments is valuable for many fields, including robotics, biomechanics, rehabilitation, and motor control. Specifically, investigating legged locomotion in compliant terrains has recently been gaining interest for the robust control of legged robots over natural environments. At the same time, the importance of ground compliance has also been highlighted in poststroke gait rehabilitation. Currently, there are not many ways to investigate walking surfaces of varying stiffness. This article introduces the variable stiffness treadmill (VST) 2, an improvement of the first version of the VST, which was the first treadmill able to vary belt stiffness. In contrast to the VST 1, the device presented in this paper (VST 2) can reduce the stiffness of both belts independently, by generating vertical deflection instead of angular, while increasing the walking surface area from 0.20 m to 0.74 m. In addition, both treadmill belts are now driven independently, while high-spatial-resolution force sensors under each belt allow for measurement of ground reaction forces and center of pressure. Through validation experiments, the VST 2 displays high accuracy and precision. The VST 2 has a stiffness range of 13 kN/m to 1.5MN/m, error of less than 1%, and standard deviations of less than 2.2 kN/m, demonstrating its ability to simulate low-stiffness environments reliably. The VST 2 constitutes a drastic improvement of the VST platform, a one-of-its-kind system that can improve our understanding of human and robotic gait while creating new avenues of research on biped locomotion, athletic training, and rehabilitation of gait after injury or disease.

The purpose of this paper is to investigate the geometrical design and path planning of Concentric tube robots (CTR) for intracerebral hemorrhage (ICH) evacuation, with a focus on minimizing the risk of damaging white matter tracts and cerebral arteries.

This paper studies the statistical concept of confidence region for a set of uncertain planar displacements with a certain level of confidence or probabilities. Three different representations of planar displacements are compared in this context and it is shown that the most commonly used representation based on the coordinates of the moving frame is the least effective. The other two methods, namely the exponential coordinates and planar quaternions, are equally effective in capturing the group structure of SE(2). However, the former relies on the exponential map to parameterize an element of SE(2), while the latter uses a quadratic map, which is often more advantageous computationally. This paper focus on the use of planar quaternions to develop a method for computing the confidence region for a given set of uncertain planar displacements. Principal component analysis (PCA) is another tool used in our study to capture the dominant direction of movements. To demonstrate the effectiveness of our approach, we compare it to an existing method called rotational and translational confidence limit (RTCL). Our examples show that the planar quaternion formulation leads to a swept volume that is more compact and more effective than the RTCL method, especially in cases when off-axis rotation is present.

This paper studies the problem of computing an average (or mean) displacement from a set of given spatial displacements using three types of parametric representations: Euler angles and translation vectors, unit quaternions and translation vectors, and dual quaternions. It is shown that the use of Euclidean norm in the space of unit quaternions reduces the problem to that of computing the mean for each quaternion component separately and independently. While the resulting algorithm is simple, a change in the sign of a unit quaternion could lead to an incorrect result. A novel kinematic measure based on dual quaternions is introduced to capture the separation between two spatial displacements. This kinematic measure is used to define the variance of a set of displacements, which is then used to formulate a constrained least squares minimization problem. It is shown that the problem decomposes into that of finding the optimal translation vector and the optimal unit quaternion. The former is simply the centroid of the set of translation vectors and the latter is obtained as the eigenvector corresponding to the least eigenvalue of a 4 × 4 positive definite symmetric matrix. In addition, it is found that the weight factor used in combining rotations and translations in the formulation does not play a role in the final outcome. Examples are provided to show the comparisons of these methods.

This work tackles practical issues which arise when using a tendon-driven robotic manipulator (TDRM) with a long, flexible, passive proximal section in medical applications. Tendon-driven devices are preferred in medicine for their improved outcomes via minimally invasive procedures, but TDRMs come with unique challenges such as sterilization and reuse, simultaneous control of tendons, hysteresis in the tendon-sheath mechanism, and unmodeled effects of the proximal section shape. A separable TDRM which overcomes difficulties in actuation and sterilization is introduced, in which the body containing the electronics is reusable and the remainder is disposable. An open-loop redundant controller which resolves the redundancy in the kinematics is developed. Simple linear hysteresis compensation and re-tension compensation based on the physical properties of the device are proposed. The controller and compensation methods are evaluated on a testbed for a straight proximal section, a curved proximal section at various static angles, and a proximal section which dynamically changes angles; and overall, distal tip error was reduced.

An exoskeleton robotic glove intended for patients who have suffered paralysis of the hand due to stroke or other factors has been developed and integrated. The robotic glove has the potential to aid patients with grasping objects as part of their daily life activities. Grasp stability was studied and researched by various research groups, but mainly focused on robotic grippers by devising conditions for a stable grasp of objects. Maintaining grasp stability is important so as to reduce the chances of the object slipping and dropping. But there was little focus on the grasp stability of robotic exoskeleton gloves, and most of the research was focused on mechanical design. A robotic exoskeleton glove was developed as well as novel methods to improve the grasp stability. The glove is constructed with rigidly coupled four-bar linkages attached to the finger tips. Each linkage mechanism has one-DOF (degree of freedom) and is actuated by a linear series elastic actuator (SEA). Two methods were developed to satisfy two of the conditions required for a stable grasp. These include deformation prevention of soft objects, and maintaining force and moment equilibrium of the objects being grasped. Simulations were performed to validate the performance of the proposed algorithms. A battery of experiments was performed on the integrated prototype in order to validate the performance of the algorithms developed.

The Magic Snake (Rubik's Snake) is a toy that was invented decades ago. It draws much less attention than Rubik's Cube, which was invented by the same professor, Erno Rubik. The number of configurations of a Magic Snake, determined by the number of discrete rotations about the elementary wedges in a typical snake, is far less than the possible configurations of a typical cube. However, a cube has only a single three-dimensional (3D) structure while the number of sterically allowed 3D conformations of the snake is unknown. Here, we demonstrate how to represent a Magic Snake as a one-dimensional (1D) sequence that can be converted into a 3D structure. We then provide two strategies for designing Magic Snakes to have specified 3D structures. The first enables the folding of a Magic Snake onto any 3D space curve. The second introduces the idea of "embedding" to expand an existing Magic Snake into a longer, more complex, self-similar Magic Snake. Collectively, these ideas allow us to rapidly list and then compute all possible 3D conformations of a Magic Snake. They also form the basis for multidimensional, multi-scale representations of chain-like structures and other slender bodies including certain types of robots, polymers, proteins, and DNA.

The simultaneous control of force and motion is important in everyday activities when humans interact with objects. While many studies have analyzed the control of movement within a perturbing force field, few have investigated its dual aspects of controlling a contact force in nonisometric conditions. The mechanism by which the central nervous system controls forces during movements is still unclear, and it can be elucidated by estimating the mechanical properties of the arm during tasks with concurrent motion and contact force goals. We investigate how arm mechanics change when a force control task is accomplished during low-frequency positional perturbations of the arm. Contrary to many force regulation algorithms implemented in robotics, where contact impedance is decreased to reduce force fluctuations in response to position disturbances, we observed a steady increase of arm endpoint stiffness as the task progressed. Based on this evidence, we propose a theoretical framework suggesting that an internal model of the perturbing trajectory is formed. We observed that force regulation in the presence of predictable positional disturbances is implemented using a position control strategy together with the modulation of the endpoint stiffness magnitude, where the direction of the endpoint stiffness ellipse's major axis is oriented toward the desired force.

This paper describes the design and control of a novel hand exoskeleton. A subcategory of upper extremity exoskeletons, hand exoskeletons have promising applications in healthcare services, industrial workplaces, virtual reality, and military. Although much progress has been made in this field, most of the existing systems are position controlled and face several design challenges, including achieving minimal size and weight, difficulty enforcing natural grasping motions, exerting sufficient grip strength, ensuring the safety of the users hand, and maintaining overall user friendliness. To address these issues, this paper proposes a novel, slim, lightweight linkage mechanism design for a hand exoskeleton with a force control paradigm enabled via a compact series elastic actuator. A detailed design overview of the proposed mechanism is provided, along with kinematic and static analyses. To validate the overall proposed hand exoskeleton system, a fully integrated prototype is developed and tested in a series of experimental trials.

[This corrects the article DOI: 10.1115/1.4032249.].

Robot-assisted minimally invasive surgery (MIS) has gained popularity due to its high dexterity and reduced invasiveness to the patient; however, due to the loss of direct touch of the surgical site, surgeons may be prone to exert larger forces and cause tissue damage. To quantify tool-tissue interaction forces, researchers have tried to attach different kinds of sensors on the surgical tools. This sensor attachment generally makes the tools bulky and/or unduly expensive and may hinder the normal function of the tools; it is also unlikely that these sensors can survive harsh sterilization processes. This paper investigates an alternative method by estimating tool-tissue interaction forces using driving motors' current, and validates this sensorless force estimation method on a 3-degree-of-freedom (DOF) robotic surgical grasper prototype. The results show that the performance of this method is acceptable with regard to latency and accuracy. With this tool-tissue interaction force estimation method, it is possible to implement force feedback on existing robotic surgical systems without any sensors. This may allow a haptic surgical robot which is compatible with existing sterilization methods and surgical procedures, so that the surgeon can obtain tool-tissue interaction forces in real time, thereby increasing surgical efficiency and safety.

In this paper, we present the design, fabrication, and testing of a robot for automatically positioning ultrasound (US) imaging catheters. Our system will point US catheters to provide real-time imaging of anatomical structures and working instruments during minimally invasive procedures. Manually navigating US catheters is difficult and requires extensive training in order to aim the US imager at desired targets. Therefore, a four-degree-of-freedom (4DOF) robotic system was developed to automatically navigate US imaging catheters for enhanced imaging. A rotational transmission enables 3DOF for pitch, yaw, and roll of the imager. This transmission is translated by the 4DOF. An accuracy analysis calculated the maximum allowable joint motion error. Rotational joints must be accurate to within 1.5 deg, and the translational joint must be accurate within 1.4 mm. Motion tests then validated the accuracy of the robot. The average resulting errors in positioning of the rotational joints were 0.04-0.22 deg. The average measured backlash was 0.18-0.86 deg. Measurements of average translational positioning and backlash errors were negligible. The resulting joint motion errors were well within the required specifications for accurate robot motion. The output of the catheter was then tested to verify the effectiveness of the handle motions to transmit torques and translations to the catheter tip. The catheter tip was navigated to desired target poses with average error 1.3 mm and 0.71 deg. Such effective manipulation of US imaging catheters will enable better visualization in various procedures ranging from cardiac arrhythmia treatment to tumor removal in urological cases.

The design of cable-driven manipulators is complicated by the unidirectional nature of the cables, which results in extra actuators and limited workspaces. Furthermore, the particular arrangement of the cables and the geometry of the robot pose have a significant effect on the cable tension required to effect a desired joint torque. For a sufficiently complex robot, the identification of a satisfactory cable architecture can be difficult and can result in multiply redundant actuators and performance limitations based on workspace size and cable tensions. This work leverages previous research into the workspace analysis of cable systems combined with stochastic optimization to develop a generalized methodology for designing optimized cable routings for a given robot and desired task. A cable-driven robot leg performing a walking-gait motion is used as a motivating example to illustrate the methodology application. The components of the methodology are described, and the process is applied to the example problem. An optimal cable routing is identified, which provides the necessary controllable workspace to perform the desired task and enables the robot to perform that task with minimal cable tensions. A robot leg is constructed according to this routing and used to validate the theoretical model and to demonstrate the effectiveness of the resulting cable architecture.

Driven by the increasing demands of the aircraft assemblage for the pose-adjustment equipment in the large-scale component docking, this paper carries out the topology synthesis of a 1-translational and 3-rotational (1T3R) four degrees of freedom (DoF) parallel manipulator with an articulated traveling plate. First, the articulated traveling plate is defined as that includes more than one rigid body articulated by one or more kinematic joints. Then, the relationship among the DoFs of the parallel manipulator and the articulated traveling plate and the number of the in-parts are proposed. According to the agreement of the arrangement way between the open-loop limbs and the in-parts, the topology synthesis procedure of the 1T3R 4-DoF parallel manipulator with an articulated traveling plate is proposed. Finally, their topology structures are obtained by discussing those of four types in terms of 1D-H, 1D-V type with opposite layout and 1D-H, 1D-V type with adjacent layout, in which the topology structures exist only for 1D-H and 1D-V type with opposite layout.

This paper presents a novel articulated drive mechanism (ADM) for a multifunctional natural orifice transluminal endoscopic surgery (NOTES) robotic manipulator. It consists mainly of three major components including a snakelike linkage, motor housing, and an arm connector. The ADM can articulate into complex shapes for improved access to surgical targets. A connector provides an efficient and convenient modularity for insertion and removal of the robot. Four DC motors guide eight cables to steer the robot. The workspace, cable displacement and force transmission relationships are derived. Experimental results give preliminary validation of the feasibility and capability of the ADM system.

In the past few years, the authors have proposed several prototypes of a able-driven upper m oskeleton () for arm rehabilitation. One of the assumptions of CAREX was that the glenohumeral joint rotation center (GH-c) remains stationary in the inertial frame during motion, which leads to inaccuracy in the kinematic model and may hamper training performance. In this paper, we propose a novel approach to estimate GH-c using measurements of shoulder joint angles and cable lengths. This helps in locating the GH-c center appropriately within the kinematic model. As a result, more accurate kinematic model can be used to improve the training of human users. An estimation algorithm is presented to compute the GH-c in real-time. The algorithm was implemented on the latest prototype of CAREX. Simulations and preliminary experimental results are presented to validate the proposed GH-c estimation method.

In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

This paper outlines the design and testing of a powered ankle prosthesis, which utilizes a four-bar mechanism in conjunction with a spring and motor that mimics nonamputee (normal) ankle moments. This approach would enable transtibial (below the knee) amputees to walk at a normal speed with minimal energy input. The design takes into account the energy supplied by the wearer required to achieve many of the desired characteristics of a normal gait. A proof-of-concept prototype prosthesis was designed, optimized, fabricated, and tested with the purpose of demonstrating its ability to match crucial ankle moments during the stance phase of gait. Testing of this prosthesis proved crucial in determining the prosthesis' capabilities and in evaluating this approach.