0

### Research Papers

J. Mechanisms Robotics. 2019;11(5):051001-051001-9. doi:10.1115/1.4043684.

The variable-stiffness joint (VSJ) plays an important role in creating compliant and powerful motions. This paper presents a novel wire-driven VSJ based on a permanent magnetic mechanism (PMM). The proposed joint regulates the joint stiffness with lower energy consumption through a wide range via the permanent magnetic mechanism. This effect possibly depends on the novel nonlinear combination of a permanent magnet-spring and wire-driven system that achieves the same stiffness with lower wire tension. A trapezoidal layout of the joint is proposed. Because of the relationship among the stiffness, the position of the joint and the stiffness of the PMM, the stiffness model is also been established. Based on this model, the decoupling controller is built to independently control the position and stiffness of the joint. Experiments show that the VSJPMM achieves position and stiffness independently and also reduces energy and power required to regulate the stiffness compared with the traditional approach. In addition, the proposed mechanism displays a powerful motion and short stiffness adjustment time.

Topics: Stiffness , Wire
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):051002-051002-9. doi:10.1115/1.4043686.

Robotic grippers, which act as the end effector and contact the objects directly, play a crucial role in the performance of the robots. In this paper, we design and analyze a new robotic gripper based on the braided tube. Apart from deployability, a self-forcing mechanism, i.e., the holding force increases with load/object weight, facilitates the braided tube as a robotic gripper to grasp objects with different shapes, weights, and rigidities. First, taking a cylindrical object as an example, the self-forcing mechanism is theoretically analyzed, and explicit formulas are derived to estimate the holding force. Second, experimental and numerical analyses are also conducted for a more detailed understanding of the mechanism. The results show that a holding force increment by 120% is achieved due to self-forcing, and the effects of design parameters on the holding force are obtained. Finally, a braided gripper is fabricated and operated on a KUKA robot arm, which successfully grasps a family of objects with varying shapes, weights, and rigidities. To summarize, the new device shows great potentials for a wide range of engineering applications where properties of the objects are varied and unpredictable.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):051003-051003-9. doi:10.1115/1.4043685.

Parallel robots have been primarily investigated as potential mechanisms with stiffness modulation capabilities through the use of actuation redundancy to change internal preload. This paper investigates real-time stiffness modulation through the combined use of kinematic redundancy and variable stiffness actuators. A known notion of directional stiffness is used to guide the real-time geometric reconfiguration of a parallel robot and command changes in joint-level stiffness. A weighted gradient-projection redundancy resolution approach is demonstrated for resolving kinematic redundancy while satisfying the desired directional stiffness and avoiding singularity and collision between the legs of a Gough/Stewart parallel robot with movable anchor points at its base and with variable stiffness actuators. A simulation study is carried out to delineate the effects of using kinematic redundancy with or without the use of variable stiffness actuators. In addition, modulation of the entire stiffness matrix is demonstrated as an extension of the approach for modulating directional stiffness.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):051004-051004-10. doi:10.1115/1.4043800.

Origami has shown its potential in designing a three-dimensional folded structure from a flat sheet of material. In this paper, we present geometric design methods to construct cylindrical and axisymmetric origami structures that can fit between two given surfaces. Due to the symmetry of the structures, a strip of folds based on the generalized Miura-ori cells is first constructed and then replicated longitudinally/circumferentially to form the cylindrical/axisymmetric origami structures. In both designs, algorithms are presented to ensure that all vertexes are either on or strictly within the region between the target surfaces. The conditions of flat-foldability and developability are fulfilled at the inner vertexes and the designs are rigid-foldable with a single degree-of-freedom. The methods for cylindrical and axisymmetric designs are similar in implementation and of potential in designing origami structures for engineering purposes, such as foldcores, foldable shelters, and metamaterials.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):051005-051005-14. doi:10.1115/1.4044067.

This paper presents the development of a new robotic tail based on a novel cable-driven universal joint mechanism. The novel joint mechanism is synthesized by geometric reasoning to achieve the desired cable length invariance property, wherein the mechanism maintains a constant length for the driving cables under universal rotation. This feature is preferable because it allows for the bidirectional pulling of the cables which reduces the requisite number of actuators. After obtaining this new joint mechanism, a serpentine robotic tail with fewer actuators, simpler controls, and a more robust structure is designed and integrated. The new tail includes two independent macro segments (2 degrees of freedom each) to generate more complex shapes (4 degrees of freedom total), which helps with improving the dexterity and versatility of the robot. In addition, the pitch bending and yaw bending of the tail are decoupled due to the perpendicular joint axes. The kinematic modeling, dynamic modeling, and workspace analysis are then explained for the new robotic tail. Three experiments focusing on statics, dynamics, and dexterity are conducted to validate the mechanism and evaluate the new robotic tail's performance.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):051006-051006-15. doi:10.1115/1.4044113.

In this paper, a lightweight high-payload cable-driven serial-parallel manipulator is proposed. The manipulator comprises one 3-degree-of-freedom (3-DOF) shoulder joint and one single-DOF elbow joint. Using a special tension-amplifying principle, which is an ingenious two-stage deceleration method, the proposed manipulator has a higher load/mass ratio than those of conventional manipulators. In this paper, the special tension-amplifying principle is discussed in detail. The shoulder and elbow joints of the proposed manipulator are driven by cables. The design of this cable-driven mechanism and the mobility of the joints are analyzed, and the structural parameters of the joints are optimized to improve the payload capacity. The size of the manipulator is close to that of a human arm because the actuators of the cable-driven mechanism can be rear-mounted. Because the elbow joint is located at the end of the shoulder joint and the driven cables of the elbow joint are coupled with the rotation of the shoulder joint, the manipulator is designed with decoupled cable routing. The overall configuration and cable routing of the manipulator are presented, and then, kinematics, joint stiffness, strength, and workspace of the manipulator are analyzed. Finally, we report on the fabrication of a physical prototype and testing of its joint stiffness, payload capacity, workspace, speed, and repeatability to verify the feasibility of our proposed manipulator.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):051007-051007-13. doi:10.1115/1.4043921.

Nowadays, translational parallel manipulators are widely used in industrial applications related to pick and place tasks. In this paper, a new architecture of a translational parallel manipulator without floating prismatic joints and without redundant constraints is presented, which leads to a robust design from the manufacturing and maintenance point of view. The frame configuration has been chosen with the aim of achieving the widest and most regular operational workspace completely free of singularities. Besides, the position equations of the proposed design are obtained in a closed form, as well as the singularity locus. It will be shown that the proposed design owns a very simple kinematics so that the related equations can be efficiently implemented in the control of the robot. In addition, the Jacobian condition number assessment shows that a wide part of the operational workspace is well-conditioned, and also the existence of an isotropic configuration will be proved. Finally, a prototype has been built by following a modular design approach.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):051008-051008-17. doi:10.1115/1.4043923.

Continuous-bodied “trunk and tentacle” robots have increased self-adaptability and obstacle avoidance capabilities, compared with traditional, discrete-jointed, robots with large rigid links. In particular, continuous-bodied robots have obvious advantages in grasping objects across a wide range of external dimensions. Not only can they grasp objects using end effectors like traditional robots, but their bodies can also be regarded as a gripping device, and large objects with respect to the robot’s scale can be captured by the entire structure of the robots themselves. Existing trunk-like robots have distributed multidrive actuation and are often manufactured using soft materials, which leads to a complex actuator system that also limits their potential applications in dangerous and extreme environments. This paper introduces a new type of elephant’s trunk robot with very few driving constraints. The robot consists of a series of novel underactuated linkage units. With a single-motor drive, the robot can achieve stable grasping of objects of different shapes and sizes. The proposed robot simplifies the requirements of the sensing and control systems during the operation process and has the advantage of accomplishing the capture task without determining the exact shape and position of the target object. It is especially suitable for operations such as non-cooperative target capture in extremely dangerous environments, including those in outer space. Based on theoretical analysis and model design, a trunk robot prototype was developed, and a comprehensive experimental study of the bending/extension and grasping operation functions was conducted to verify the validity of the proposed robot design.

Topics: Robots , Motors , Engines
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):051009-051009-9. doi:10.1115/1.4043924.

According to Camus’ theorem, for a single degree-of-freedom (DOF) three-body system with the three instant centers staying coincident, a point embedded on a body traces a pair of conjugated curves on the other two bodies. This paper discusses a fundamental issue not addressed in Camus’ theorem in the context of higher order curvature theory. Following the Aronhold–Kennedy theorem, in a single degree-of-freedom three-body system, the three instant centers must lie on a straight line. This paper proposes that if the line of the three instant centers is stationary (i.e., slide along itself) on the line of the instant centers, a point embedded on a body traces a pair of conjugated curves on the other two bodies. Another case is that if the line of the three instant centers rotates about a stationary point, the stationary point embedded on a body also traces a pair of conjugated curves on the other two bodies. The paper demonstrates the use of instantaneous invariants to synthesize such a three-body system leading to a conjugate curve-pair generation. It is a supplement or extension of Camus’ theorem. Camus’ theorem may be regarded as a special singular case, in which all three instant centers are coincident.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):051010-051010-8. doi:10.1115/1.4043925.

This paper presents a novel three degrees-of-freedom (DOF) compliant parallel mechanism (CPM) with a fully decoupled spatial motion ($θX−θY−Z$) and optimized mechanical properties. To design the CPM using the beam-based structural optimization method, several novel criteria for synthesizing three-legged CPMs with fully decoupled motions are derived. The obtained results suggest that the synthesized CPM delivers a diagonal compliance matrix, a large workspace of $10deg×10deg×7mm$, fast dynamic response of $∼100Hz$, and good stiffness performance whereby the translational and rotational stiffness ratios are ∼3600 and ∼570, respectively. A prototype of the synthesized CPM is fabricated using one of the three-dimensional (3D) printing technologies, electron beam melting (EBM). Experimental results have shown that the 3D printed CPM can produce the full workspace with deterministic mechanical properties whereby the highest deviations between the theoretical and experimental results are $11.2%$ and $1%$ for stiffness and dynamic behaviors, respectively. Importantly, the decoupled-motion characteristic is also verified via an energy approach, i.e., the energies of the undesired parasitic motions are minor ($<1%$) as compared with the energy of the desired motion. In addition, several comparisons are conducted to clarify the advantages of the synthesized CPM to the existing designs. All these investigations suggest that the proposed CPM can be used in precision positioning systems due to the good stiffness characteristics, large workspace, fast dynamic response, and decoupled output motions.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):051011-051011-17. doi:10.1115/1.4044004.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):051012-051012-12. doi:10.1115/1.4044163.

This paper presents the design, analysis, and testing of a novel multimodal grasper having the capabilities of shape conformation, within-hand manipulation, and a built-in compact mechanism to vary the forces at the contact surface. The proposed grasper has two important qualities: versatility and less complexity. The former refers to the ability to grasp a range of objects having different geometrical shape, size, and payload and perform in-hand manipulations such as rolling and sliding, and the latter refers to the uncomplicated design, and ease of planning and control strategies. Increasing the number of functions performed by the grasper to adapt to a variety of tasks in structured and unstructured environments without increasing the mechanical complexity is the main interest of this research. The proposed grasper consists of two hybrid jaws having a rigid inner structure encompassed by a flexible, active gripping surface. The flexibility of the active surface has been exploited to achieve shape conformation, and the same has been utilized with a compact mechanism, introduced in the jaws, to vary the contact forces while grasping and manipulating an object. Simple and scalable structure, compactness, low cost, and simple control scheme are the main features of the proposed design. Detailed kinematic and static analysis are presented to show the capability of the grasper to adjust and estimate the contact forces without using a force sensor. Experiments are conducted on the fabricated prototype to validate the different modes of operation and to evaluate the advantages of the proposed concept.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):051013-051013-12. doi:10.1115/1.4044162.

Recently, a new concept for continuum robots capable of producing macro-scale and micro-scale motion has been presented. These robots achieve their multi-scale motion capabilities by coupling direct actuation of push-pull backbones for macro-motion with indirect actuation whereby the equilibrium pose is altered to achieve micro-scale motion. This paper presents a first attempt at explaining the micro-motion capabilities of these robots from a modeling perspective. This paper presents the macro- and micro-motion kinematics of a single-segment continuum robot by using statics coupling effects among its subsegments. Experimental observations of the micro-scale motion demonstrate a turning point behavior which could not be explained well using the current modeling methods. We present a simplistic modeling approach that introduces two calibration parameters to calibrate the moment coupling effects among the subsegments of the robot. It is shown that these two parameters can reproduce the turning point behavior at the micro-scale. The instantaneous macro- and micro-scale kinematics Jacobians and the calibration parameters identification Jacobian are derived. The modeling approach is verified against experimental data showing that our simplistic modeling approach can capture the experimental motion data with the RMS position error of 5.82 μm if one wishes to fit the entire motion profile with the turning point. If one chooses to exclude motions past the turning point, our model can fit the experimental data with an accuracy of 4.76 μm.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Mechanisms Robotics. 2019;11(5):054501-054501-8. doi:10.1115/1.4044002.

This paper puts forward a linear variable stiffness joint (VSJ) based on the electromagnetic principle. The VSJ is constituted by an annular permanent magnet (PM) and coaxial cylindrical coil. The output force and stiffness are linearly proportional to the coil current. In consequence, the stiffness adjustment motor and mechanisms required by many common designs of VSJs are eliminated. A physical prototype of the electromagnetic VSJ is manufactured and tested. The results indicate that the prototype can achieve linear force-deflection characteristics and rapid stiffness variation response. Using an Arduino and H-bridge driver board, the electromagnetic compliance control system is developed in order to realize the precise control of the interaction force. The static force control error is no more than ±0.5 N, and the settling time can be controlled within only 40 ms. At last, an experiment of squeezing the raw egg is conducted. The experiment intuitively exhibits the performance of electromagnetic compliance in stable force control and keeping safe robot-environment interaction.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(5):054502-054502-7. doi:10.1115/1.4043818.

The energy balancing concept seeks to reduce actuation requirements for a morphing structure by strategically locating negative stiffness devices to tailor the required deployment forces and moments. One such device is the spiral pulley negative stiffness mechanism. This uses a cable connected with a pre-tension spring to convert the decreasing spring force into the increasing balanced torque. The kinematics of the spiral pulley is first developed for bidirectional actuation, and its geometry is then optimized by employing an energy conversion efficiency function. The performance of the optimized bidirectional spiral pulley is then evaluated through the net torque, the total required energy, and energy conversion efficiency. Then, an additional test rig tests the bidirectional negative stiffness property and compares the characteristics with the corresponding analytical result. Exploiting the negative stiffness mechanism is of significant interest not only in the field of morphing aircraft but also in many other energy and power reduction applications.

Commentary by Dr. Valentin Fuster