Research Papers

J. Mechanisms Robotics. 2019;11(3):031001-031001-8. doi:10.1115/1.4042631.

Trajectory planning and an efficient control scheme play a crucial role in improving the performance of pick-and-place robots. This paper introduces a novel method of trajectory planning with cycle time and path constraints. Assuming that a smooth trajectory is given, to be followed within a prescribed cycle time, the newly proposed method of trajectory planning removes the torque peaks of the actuators by a suitable scheduling of the velocity of the moving plate. Since pick-and-place robots are usually expected to meet the end poses in a certain time span, while disregarding the intermediate poses, the velocity can be tuned properly around the critical points of the trajectory by means of a time-scaling function. Moreover, the authors report the formulation of a linear quadratic regulator (LQR) controller with normalized variables to be used in conjunction with our trajectory-tracking control scheme for an in-house-developed Schönflies-motion generator. This parallel robot offers a functionally symmetric, single-loop architecture, with an isostatic kinematic chain, and virtually unlimited rotatability of its gripper. A comparison between two actuation systems developed by the authors is conducted via simulation results.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031002-031002-7. doi:10.1115/1.4043044.

Arch-profiles of bistable arches, in their two force-free equilibrium states, are related to each other. This bilateral relationship is derived for arches with fixed–fixed boundary conditions in two forms: a nonlinear single-variable equation for analysis and a closed-form analytical expression for design. Some symmetrical features of shape as well as necessary and sufficient conditions for bistability are presented as corollaries. Analysis and design of arch-profiles using the bilateral relationship are illustrated through examples.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031004-031004-8. doi:10.1115/1.4043048.

Rigid foldability is an important requirement when origami is used as the basis to design technical systems that consist of rigid materials. This paper presents a heuristic algorithm that adjusts the location of vertices of nonrigidly foldable but kinematically determinate crease patterns such that they become rigidly foldable. The adjustment is achieved by utilizing constraint violations that occur during the folding process of nonrigidly foldable configurations. The folding process is kinematically simulated through a robust simulator that is based on a bar and hinge principle. The benefits of the algorithm are showcased in different examples, including single-vertex as well as multi-vertex crease patterns.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031005-031005-11. doi:10.1115/1.4043047.

Taking the well-known Tricept robot as an example, this paper presents a semi-analytical approach for elastodynamic modeling of five or six degrees of freedom (DOF) hybrid robots composed of a 3-DOF parallel mechanism plus a 2- or 3-DOF wrist. Drawing heavily on screw theory combined with structural dynamics, the kinetic and elastic potential energies of the parallel mechanism and of the wrist are formulated using the dual properties of twist/wrench systems and a static condensation technique. This results in a 9-DOF dynamic model that enables the lower-order dynamic behavior over the entire workspace to be estimated in a very efficient and accurate manner. The lower-order natural frequencies and mode shapes estimated by the proposed approach are shown to have very good agreement with those obtained by a full-order finite element (FE) model. It thus provides a very time-effective tool for optimal design within a virtual prototyping framework for hybrid robot-based machine tools.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031006-031006-10. doi:10.1115/1.4043050.

Research on formation control and cooperative localization for multirobot systems has been an active field over the last years. A powerful theoretical framework for addressing formation control and localization, especially when exploiting onboard sensing, is that of formation rigidity (mainly studied for the cases of distance and bearing measurements). Rigidity of a formation depends not only on the topology of the sensing/communication graph but also on the spatial arrangement of the robots, since special configurations (“singularities” of the rigidity matrix), which are hard to detect in general, can cause a rigidity loss and prevent convergence of formation control/localization algorithms based on formation rigidity. The aim of this paper is to gain additional insights into the internal structure of bearing rigid formations by considering an alternative characterization of formation rigidity using tools borrowed from the mechanical engineering community. In particular, we show that bearing rigid graphs can be given a physical interpretation related to virtual mechanisms, whose mobility and singularities can be analyzed and detected in an analytical way by using tools from the mechanical engineering community (screw theory, Grassmann geometry, and Grassmann-Cayley algebra). These tools offer a powerful alternative to the evaluation of the mobility and singularities typically obtained by numerically determining the spectral properties of the bearing rigidity matrix (which typically prevents drawing general conclusions). We apply the proposed machinery to several case formations with different degrees of actuation and discuss known (and unknown) singularity cases for representative formations. The impact on the localization problem is also discussed.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031007-031007-14. doi:10.1115/1.4043046.

A general method for the analytical elastostatic stiffness modeling of overconstrained parallel manipulators (PMs) using geometric algebra and strain energy is proposed. First, an analytical solution of the constraint and actuation wrenches exerted on the moving platform is obtained using the outer product and dual operation of geometric algebra, which avoids solving complex symbolic linear equations. Second, considering the compliances of the limbs, an analytical elastostatic model is established using the strain energy to obtain the stiffness matrices of the limbs. Finally, the deformation compatibility equations are added into equilibrium equations to obtain the overall stiffness matrix of the PM, which has a concise expression and a clear physical meaning. The proposed method is applied to the Tex3 overconstrained PM and the Tex4 overconstrained PM with redundant actuation to prove its validity. Comparable results between the theoretical analysis and the finite-element analysis (FEA) show that the former could be used as an effective alternative to the FEA method in the predesign stage. This new approach is universally applicable to the elastostatic stiffness analysis of overconstrained PMs.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031008-031008-9. doi:10.1115/1.4043215.

The kinematics has attracted continuous interests in the field of robotics. Terminal position and orientation coupling phenomenon is the key problem and the first consideration in the kinematics of lower mobility robots. However, this property was usually neglected or has not been well solved. This paper discusses the terminal position and orientation coupling issues in lower mobility robots, especially for the lower mobility hybrid robots. First, this paper reveals the terminal position and orientation coupling in serial and parallel robots. Then, based on elimination theory, an approach for establishing the terminal position and orientation coupling equations for hybrid robots is proposed, which is illustrated in detail by the (3-RPS) + (RR) and (3-RPS) + (3-RCR) hybrid robots. The results show that the hybrid robots have highly nonlinear terminal position and orientation coupling relations, which are more complicated than serial and parallel robots. The research of this paper is valuable in kinematics modeling of robots.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031009-031009-13. doi:10.1115/1.4043023.

We present a hand specialized for climbing unstructured rocky surfaces. Articulated fingers achieve grasps commonly used by human climbers. The gripping surfaces are equipped with dense arrays of spines that engage with asperities on hard rough materials. A load-sharing transmission system divides the shear contact force among spine tiles on each phalanx to prevent premature spine slippage or grasp failure. Taking advantage of the hand’s kinematic and load-sharing properties, the wrench space of achievable forces and moments can be computed rapidly. Bench-top tests show agreement with the model, with average wrench space errors of 10–15%, despite the stochastic nature of spine/surface interaction. The model provides design guidelines and control strategy insights for the SpinyHand and can inform future work.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031010-031010-10. doi:10.1115/1.4042849.

We present a novel 4-DOF (degrees of freedom) parallel robot designed for five-axis micromachining applications. Two of its five telescoping legs operate simultaneously, thus acting as an extensible parallelogram linkage, and in conjunction with two other legs control the position of the tooltip. The fifth leg controls the tilt of the end-effector (a spindle), while a turntable fixed at the base of the robot controls the swivel of the workpiece. The robot is capable of tilting its end-effector up to 90 deg, for any tooltip position. In this paper, we study the mobility of the new parallel kinematic machine (PKM), describe its inverse and direct kinematic models, then study its singularities, and analyze its workspace. Finally, we propose a potential mechanical design for this PKM utilizing telescopic actuators as well as the procedure for optimizing it. In addition, we discuss the possibility of using constant-length legs and base-mounted linear actuators in order to increase the volume of the workspace.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031011-031011-9. doi:10.1115/1.4042632.

Fiber reinforced elastomeric enclosures (FREEs) are soft pneumatic representative elements that can form the basis for building soft self-actuating structures/mechanisms. When placed in different configurations, they exhibit unique stroke amplification characteristics that can be leveraged to create interesting deformation patterns. Such deformations occur as a combination of axial and bending deflection due to internal pressurization and external forces. This paper presents a lumped reduced-order model that enables quick and accurate analysis of mechanisms made from FREEs grouped as a system. The model proposed is a modified four-spring pseudo-rigid-body (PRB) model that effectively captures the axial and bending stiffnesses of contracting FREEs. Parametric estimation of the model is performed using a multistart optimization routine to fit the PRB model with results from experiments and finite element analysis (FEA). The model is also generalized and statistically verified for FREEs with different fiber angles, length-to-diameter ratios, and different actuation pressures. Finally, efficacy of the approach is validated through three case studies that involve a planar arrangement of FREEs at different orientations.

J. Mechanisms Robotics. 2019;11(3):031012-031012-9. doi:10.1115/1.4042629.

The parallel mechanism with a reconfigurable platform retains all advantages of parallel mechanisms and provides additional functions by virtue of the reconfigurable platform, leading to kinematic coupling between limbs that restricts development of the mechanism. This paper aims at dealing with kinematic coupling between limbs by investigating the transferability of limb constraints and their degrees of relevance to the platform constraints based on the geometric model of the mechanism. The paper applies screw-system theory to verifying the degree of relevance between limb constraint wrenches and platform constraint wrenches, and reveals the transferability of limb constraints, to obtain the final resultant wrenches and twists of the end effector. The proposed method is extended to parallel mechanisms with planar n-bar reconfigurable platforms, spherical n-bar reconfigurable platforms, and other spatial reconfigurable platforms and lends itself to a way of studying a parallel mechanism with a reconfigurable platform.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031013-031013-8. doi:10.1115/1.4042633.

This paper develops a geometric method to estimate the error space of 3-DOF planar mechanisms with the Minimum Volume Ellipsoid Enclosing (MVEE) approach. Both the joint clearances and actuator errors are considered in this method. Three typical planar parallel mechanisms are used to demonstrate. Error spaces of their serial limbs are analyzed. Thereafter, limb-error-space-constrained mobility of the manipulator, namely, the manipulator error space is analyzed. The MVEE method has been applied to simplify the constraint modeling. A closed-form expression for the manipulator error space is derived. The volume of the manipulator error space is numerically estimated. The approach in this paper is to develop a geometric error analysis method of parallel mechanisms with clear algebraic expressions. Moreover, no forward kinematics computations have been performed in the proposed method, in contrast to the widely used interval analysis method. Although the estimated error space is larger than the actual one, because the enclosing ellipses enlarge the regions of limb error space, the method has an attractive advantage of high computational efficiency.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031014-031014-12. doi:10.1115/1.4043214.

A diamond origami pattern is a well-known origami pattern consisting of identical six-crease vertices. As each vertex can be modeled as a spherical 6R linkage with three degrees of freedom (DOF), the tessellated pattern with multiple vertices is a multi-DOF system, which makes it difficult to fully control the motion in the desired symmetric manner. Here, two splitting schemes on the diamond vertex are proposed to generate three types of unit patterns to reduce the DOF. This vertex-splitting technique is applied to the multivertex diamond origami pattern to produce several one-DOF basic assemblies, which form a number of one-DOF origami patterns. Two of the one-DOF origami patterns are discussed: one of which is a flat-foldable origami pattern mixed with four- and six-crease vertices and the other is a nonflat-foldable one mixed with four-, five-, and six-crease vertices. In the one-DOF patterns, the symmetrically kinematic property of the original diamond origami pattern is well kept. Such property would significantly facilitate engineering applications comparing to the multi-DOF origami patterns. It also paves a new road to construct one-DOF origami patterns.

Topics: Diamonds , Linkages
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031015-031015-7. doi:10.1115/1.4042627.

This paper presents a method for topology optimization of large-deflection compliant mechanisms with multiple inputs and outputs by considering the coupling issue. First, the objectives of the design problem are posed by modeling the output loads using several springs to enable control of the input–output behavior. Second, a scheme is proposed to obtain a completely decoupled mechanism. Both input coupling and output coupling are considered. Third, with the implementation of an energy interpolation scheme to stabilize the numerical simulations, the geometrical nonlinearity is considered to appropriately capture the large displacements of compliant mechanisms. Finally, several numerical examples are presented to demonstrate the validity of the proposed method. Comparison studies with the obtained results without considering the coupling issues are also presented.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):031016-031016-10. doi:10.1115/1.4042628.

Two rotations and one translation (2R1T) parallel kinematic machines (PKMs) are suitable for the machining of complex curved surfaces, which requires high speed and precision. To further improve rigidity, precision, and avoid singularity, actuation redundancy, and overconstrained PKMs with fixed actuators and limited-degrees of freedom (DOF) limbs are preferred. However, there are few 2R1T PKMs with these features. This paper introduces a new 2R1T overconstrained PKM with actuation redundancy, which is called Tex4. The Tex4 PKM consists of four limited-DOF limbs; that is, two PUR limbs and two 2PRU limbs (where P denotes an actuated prismatic joint, U denotes a universal joint, and R denotes a revolute joint). The kinematic model of the proposed 2PUR-2PRU machine is presented along with the results of mobility, inverse kinematics, and velocity analysis. By considering the motion/force transmissibility, the dimensional parameters of the Tex4 PKM were optimized to obtain an improved satisfactory transmission workspace without singular configurations. Finally, a prototype based on the optimized parameters was fabricated, and its feasibility and accuracy were validated by motion and position error experiments. The Tex4 PKM has the advantages of high rigidity, simple kinematic model, and zero singularity in the workspace, which suggests that it has potential for use in the high-speed machining of curved surfaces.

Commentary by Dr. Valentin Fuster

Design Innovation Paper

J. Mechanisms Robotics. 2019;11(3):031003-031003-7. doi:10.1115/1.4043024.

In this paper, a fabric-based wearable soft robotic limb (SRL) is presented. It can be worn on the user’s body to potentially assist with activities of daily living. This SRL can perform a bidirectional bending motion by inflating the pneumatic bending actuators. The end effector, which is a fabric-based soft gripper, can pick up small objects in daily life. The SRL is pneumatically actuated, and its bending motion and payload capability were characterized. All the actuation and control systems are integrated in a portable control box. The SRL can be voice-controlled using an Android-based voice recognition mobile application. We expect the SRL to be a promising wearable tool that can assist the user in managing simple activities in daily living, while allowing the user’s natural human hands to work on more complex tasks.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):035001-035001-8. doi:10.1115/1.4042626.

In the field of milli-robots, several methods of constructing robots by laminating materials and then folding have been developed. Among these methods, smart composite microstructures (SCM) is widely used for making lightweight small mobile robots. However, in the case of a robot manufactured by the SCM method, due to flexible and easily deformable links and joints, it is often difficult to obtain proper kinematic movement due to deformation of the structure when a heavy load is applied. In this paper, studies on the mechanism design and manufacturing were carried out to increase the load capacity of robots manufactured by SCM. First, we modified the kinematics of the robot to reduce off-axis loading on flexure joints by using a planar 6 bar leg mechanism, which was fabricated using a new multilayer SCM process. Second, the fabrication process is improved to reduce peeling of laminate structures by introducing integrated rivets at joints. Finally, alternative materials, such as balsa, are used. To verify the design and fabrication improvements, we compared the payloads after applying the proposed methods to an existing cockroach robot design. Compared to the previous design, speed with a 50-g payload increased from 7 to 30 cm per second.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):035002-035002-9. doi:10.1115/1.4043051.

PUFFER (“pop-up flat-folding explorer robot”) is an expendable, two-wheeled NASA/JPL rover that is meant to explore the less-accessible regions of Mars. This paper presents the UC Berkeley prototype of PUFFER that was used to inform the mechanical design of the folding chassis for the ensuing NASA/JPL version. PUFFER is so named because it can fold itself to fit into tight spaces; its chassis consists of a 3-D linkage that can vary the sprawl angle of its wheels. This ability to sprawl, besides letting multiple PUFFERs fit into a parent rover, improves PUFFER’s slope-climbing ability by allowing it to lower its center of mass. To further improve slope climbing, each wheel is fitted out with nitinol brushes that serve to enhance ground traction. Together, these two features allow the Berkeley prototype of PUFFER to climb 47 deg rock inclines that have a surface roughness of about half its folded height. Other qualities of PUFFER are that it has a collapsible tail, is able to flip itself over, and requires only three actuators.

Topics: Design , Traction , Wheels , Linkages , Wire
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):035003-035003-8. doi:10.1115/1.4042630.

The soft grippers driven by pneumatics have an advantage of effectively lifting soft materials and heavier objects with clean air. They provide multiplanar compliant stability when compared with standard claw-like grippers because of the larger contact area. Such grippers can work on objects with a greater surface area than the gripper itself. However, until now, to enhance the gripping on heavier objects, multiple suction cups are used, which involve tubing and a vacuum pump for each individual cup, which ultimately makes the setup bulky and immovable. Furthermore, using a bigger suction gripper requires bigger tubing and higher negative pressure. To tackle this limitation, we are introducing layer-jamming suction grippers with kirigami pattern for stiffness tuning. The kirigami-patterned base and sheets make a channel from the air tubing to each hole that acts as multiple suction cups. The sheets incorporated within the suction cups, working as layer-jamming, control the stiffness of the prototype. Results highlight that the gripper has the capability of lifting 200 times its own weight with a planar surface and has a strength and durability to withstand a maximum force of 87 N. One important characteristic of the gripper is its adaptability to the curved surfaces, which has an enhanced grasp and is able to lift 154 times its own weight. The ease of fabrication, low cost, and higher lifting capabilities open up a wide area of opportunities to see the advancements in technologies with the suction grippers.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Mechanisms Robotics. 2019;11(3):034501-034501-5. doi:10.1115/1.4043049.

The static balancing of mechanical systems is an important issue because it allows one to significantly decrease the size of actuators for equivalent displacements of the end effector. Indeed, the actuators do not have to produce the required input energy to counterbalance the variation of the potential energy of the robot. However, the literature review shows that in many cases the gravity balancing of mechanical systems is carried out by neglecting the masses of auxiliary links associated with the principal mechanism. For many balancing schemes, it is a source of errors.

This paper deals with an improved solution for gravity compensators based on the inverted slider-crank mechanism considering the masses of the coupler and the spring. To achieve this, the torques are determined due to auxiliary links. Subsequently, they are introduced into the balancing equation for minimization of the residual unbalance. Hence, a more accurate balancing of gravity compensators based on the inverted slider-crank mechanism can be achieved. The efficiency of the suggested approach is illustrated by numerical simulations.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):034502-034502-9. doi:10.1115/1.4043043.

Accurate and robust force control is still a great challenge for robot–environment contact applications, such as in situ repair, polishing, and assembly. To tackle this problem, this paper proposes a force control joint with a parallel configuration, including two identical four-bar linkages driven by linear springs to push up the output end of the joint, and a parallel-connected pneumatic artificial muscle (PAM) to pull down its output end. In the new design, the link length of the linkages will be optimized to make the difference between the profile of the linkage and that of PAM constant within the limits of the joint given the force–displacement profile of PAM at a certain level of its input pressure. Furthermore, PAM's nonlinear hysteresis effect, which is believed to limit the accuracy of the joint's force control, will be represented by a new dynamics model that is to be developed from the classical Bouc–Wen (BW) hysteresis model. Simulation tests are then conducted to reveal that the adoption of the PAM hysteresis model yields improved accuracy of force control, and a series of curve trajectory tracking experiments are performed on a six-joint universal industrial robot to verify that the parallel force control joint is capable to enhance force control accuracy for robot contact applications.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2019;11(3):034503-034503-5. doi:10.1115/1.4043371.

It is well understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs well in one particular Euclidean coordinate frame then it should be expected to perform identically if that coordinate frame is arbitrarily rotated or scaled. Similarly, the performance of the system should not be affected if its key parameters are all consistently defined in metric units or in imperial units. In this paper we show that a recently introduced generalized matrix inverse permits performance consistency to be rigorously guaranteed in control systems that require solutions to underdetermined and/or overdetermined systems of equations. We analyze and empirically demonstrate how these theoretical guarantees can be directly obtained in a practical robotic arm system.

Commentary by Dr. Valentin Fuster

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