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### Guest Editorial

J. Mechanisms Robotics. 2009;2(1):010301-010301-2. doi:10.1115/1.4000757.
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At the Mechanisms & Robotics Awards Luncheon held September 2, 2009 in San Diego, CA, Dr. Larry L. Howell, Professor of Mechanical Engineering at Brigham Young University, received the 2009 ASME Mechanisms & Robotics Award. At the luncheon, Professor Howell distributed copies of a compilation of essays from the ASME Mechanisms & Robotics community and the compilation was accompanied by the following comments.

Commentary by Dr. Valentin Fuster

### Research Papers

J. Mechanisms Robotics. 2009;2(1):011001-011001-10. doi:10.1115/1.4000518.

The singularity-free workspace of parallel mechanisms is highly desirable in a context of robot design. This work focuses on analyzing the effects of the orientation angles on the singularity-free workspace of the Gough–Stewart platform in order to determine the optimal orientation. In any orientation with $ϕ=θ=0 deg$ and $ψ≠±90 deg$, the singularity surface becomes a plane coinciding with the base plane. Hence, an analytic algorithm is presented in this work to determine the singularity-free workspace. The results show that the singularity-free workspace in some orientations can be larger than that in the reference orientation with $ϕ=θ=ψ=0 deg$. However, the global optimal orientation is difficult to determine. Only an approximate optimal orientation is available. The results obtained can be applied to the design or parameter setup of the Gough–Stewart platform.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2009;2(1):011002-011002-8. doi:10.1115/1.4000521.

The autoderivation of valid topological graph (TGs) of planar 3DOF parallel mechanisms is studied systematically based on topology embryonic graphs (TEGs) and arrays. First, some TEGs without any binary links are constructed, some paths with only binary links are distributed over the TEGs, and some valid TGs of the planar 3DOF PMs are derived. Second, a complicated derivation of the TG is transformed into an easy derivation of array. Third, some programs are compiled in VB, all valid arrays corresponding to nonisomorphic TGs are derived automatically, and some invalid arrays corresponding to the isomorphic TGs and invalid TGs are determined by compiled programs. Finally, many valid TGs of planar 3DOF PMs with various basic links are derived from valid arrays.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2009;2(1):011003-011003-9. doi:10.1115/1.4000523.

Lamina emergent mechanisms (LEMs) are fabricated from planar materials (lamina) and have motion that emerges out of the fabrication plane. LEMs provide an opportunity to create compact, cost-effective devices that are capable of accomplishing sophisticated mechanical tasks. They offer the advantages of planar fabrication, a flat initial state (compactness), and monolithic composition (which provides the advantages associated with compliant mechanisms). These advantages come with the tradeoff of challenging design issues. LEM challenges include large, nonlinear deflections, singularities due to two possible motion configurations as they leave their planar state, and coupling of material properties and geometry in predicting mechanism behavior. This paper defines lamina emergent mechanisms, motivates their study, and proposes a fundamental framework on which to base future LEM design. This includes the fundamental components (created by influencing geometry, material properties, and boundary conditions) and basic mechanisms (including planar four-bars and six-bars, and spherical and spatial mechanisms).

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2009;2(1):011004-011004-9. doi:10.1115/1.4000524.

This paper presents a minimal invariant coordinate-free description of rigid body motion trajectories. Based on a motion model for the instantaneous screw axis, a time-based coordinate-free description consisting of six scalar functions of time is defined. Analytical formulas are presented to obtain these functions from the pose or twist coordinates of a motion trajectory. The time-based functions are then stripped from their temporal information yielding five independent geometric functions together with a scalar motion profile. The geometric functions are shown to be invariant with respect to time scale, linear and angular scale, motion profile, reference frame, and reference point on the rigid body used to express the translational components of the motion. An algorithm is given to reconstruct a coordinate representation of a motion trajectory from its coordinate-free description. A numerical example illustrates the validity of the approach.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2009;2(1):011005-011005-8. doi:10.1115/1.4000527.

This paper shows how to generate underactuated manipulators by substituting nonholonomic spherical pairs for (holonomic) spherical pairs in ordinary (i.e. not underactuated) manipulators. As a case study, an underactuated manipulator, previously proposed by one of the authors, is demonstrated to be generated, through this pair substitution from an inversion of the 6-3 fully parallel manipulator. Moreover, the kinetostatic analysis of this underactuated manipulator is reconsidered, and a simple and compact formulation is obtained. The results of this kinetostatic analysis can be used both in the design of the underactuated manipulator and in its control.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2009;2(1):011006-011006-13. doi:10.1115/1.4000519.

This paper presents a novel and unified analytic formulation for kinematics, statics, and shape restoration of multiple-backbone continuum robots. These robots achieve actuation redundancy by independently pulling and pushing three backbones to carry out a bending motion of two-degrees-of-freedom (DoF). A solution framework based on constraints of geometric compatibility and static equilibrium is derived using elliptic integrals. This framework allows the investigation of the effects of different external loads and actuation redundancy resolutions on the shape variations in these continuum robots. The simulation and experimental validation results show that these continuum robots bend into an exact circular shape for one particular actuation resolution. This provides a proof to the ubiquitously accepted circular-shape assumption in deriving kinematics for continuum robots. The shape variations due to various actuation redundancy resolutions are also investigated. The simulation results show that these continuum robots have the ability to redistribute loads among their backbones without introducing significant shape variations. A strategy for partially restoring the shape of the externally loaded continuum robots is proposed. The simulation results show that either the tip orientation or the tip position can be successfully restored.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2009;2(1):011007-011007-9. doi:10.1115/1.4000525.

Micromanipulators play an important role in the precision engineering field from optical stages to micro-electromechanical systems for their excellent performances. In this paper, a 6-DOF perpendicular parallel micromanipulator (PPMM) is proposed and its prototype is developed. The isotropy and decoupled characteristics of the 6-DOF PPMM are discussed. The relationship among input-force, payload, stiffness, and displacement (IPSD) of the 6-DOF PPMM is studied and the model of the relationship among the IPSD is derived in an analytical style. The relation between voltage value of piezoelectric actuator and output displacement is obtained base on an IPSD model. Finally, the simulations by finite element method and the test of the prototype of the 6-DOF PPMM are performed. Compared with the results of simulations and the test, the feasibility of IPSD model is verified. The proposed model is useful for both digital control of the 6-DOF PPMMs and design of the micromanipulators.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2009;2(1):011008-011008-8. doi:10.1115/1.4000528.

The kinematics of the octopus’s arm is studied from the point of view of robotics. A continuum three-dimensional kinematic model of the arm, based on a nonlinear rod theory, is proposed. The model enables the calculation of the strains in various muscle fibers that are required in order to produce a given configuration of the arm—a solution to the inverse kinematics problem. The analysis of the forward kinematics problem shows that the strains in the muscle fibers at two distinct points belonging to a cross section of the arm determine the curvature and the twist of the arm at that cross section. The octopus’s arm lacks a rigid skeleton and the role of material incompressibility in enabling the configuration control is studied.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2009;2(1):011009-011009-5. doi:10.1115/1.4000520.

Due to Cayley’s theorem the line $s∊Σ$ ($=moving$ system) spanned by the centers of the spherical joints of a revolute-spherical-spherical-revolute linkage generates a surface of degree 8. In the special case of parallel rotary axes of the R-joints the corresponding ruled surface is only of degree 6. Now the point locus of any point $X∊Σ\{s}$ is a surface of order 16 (general case) or of order 12 (special case). Hunt (1978, Kinematic Geometry of Mechanisms, Clarendon, Oxford) suggested that the circularity of this so called spin-surface for the general case is 8 and this was later proved. We demonstrate that the circularity of the spin-surface for the special case is 4 instead of 6 as given in the literature (1994, “The (True) Stewart Platform Has 12 Configurations,” Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2160–2165). As a consequence generalized triangular symmetric simplified manipulators (the three rotary axes need not be coplanar) with two parallel rotary joints can have up to 16 solutions instead of 12 (2006, Parallel Robots, 2nd ed., Springer, New York). We show that this upper bound cannot be improved by constructing an example for which the maximal number of assembly modes is reached. Moreover, we list all parallel manipulators of this type where more than $4×2=8$ points are located on the imaginary spherical circle.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2009;2(1):011010-011010-10. doi:10.1115/1.4000558.

This paper presents a new geometry-based method to determine if a cable-driven robot operating in a $d$-degree-of-freedom workspace $(2≤d≤6)$ with $n≥d$ cables can generate a given set of wrenches in a given pose, considering acceptable minimum and maximum tensions in the cables. To this end, the fundamental nature of the available wrench set is studied. The latter concept, defined here, is closely related to similar sets introduced by Ebert-Uphoff and co-workers (2004, “Force-Feasible Workspace Analysis for Underconstrained, Point-Mass Cable Robots,” IEEE Trans. Rob. Autom., 5, pp. 4956–4962; 2007, “Workspace Optimization of a Very Large Cable-Driven Parallel Mechanism for a Radiotelescope Application,” Proceedings of the ASME IDETC/CIE Mechanics and Robotics Conference, Las Vegas, NV). It is shown that the available wrench set can be represented mathematically by a zonotope, a special class of convex polytopes. Using the properties of zonotopes, two methods to construct the available wrench set are discussed. From the representation of the available wrench set, computationally efficient and noniterative tests are presented to verify if this set includes the task wrench set, the set of wrenches needed for a given task.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2010;2(1):011011-011011-9. doi:10.1115/1.4000517.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2010;2(1):011012-011012-10. doi:10.1115/1.4000522.

The precision of parallel robots is limited by backlash in their joints. This paper investigates algorithms for designing inexpensive planar parallel robots with prescribed backlash-free workspace. The method of closing the backlash of the actuators uses preloaded flexible joints to replace the passive joints. These flexible joints may be made using standard joints with preloaded springs or by using preloaded flexure joints. Given a norm-bounded wrench acting on the robot, an algorithm is presented for determining the required preload for the flexible joints in order to guarantee backlash-free operation along a path or within a prescribed workspace. An investigation of the effects of the preloaded flexible joints on the stiffness is carried out using performance measures comparing the same robot with or without preloaded joints. These performance measures use an extended stiffness definition based on three noncollinear vertices on the moving platform. This paper presents simulations of the statics, stiffness, and backlash prevention algorithm, followed by experimental validations.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2010;2(1):011013-011013-14. doi:10.1115/1.4000526.

In this paper we present the force distribution analysis for a dual input actuator called parallel force/velocity actuator (PFVA). We present five physical quantities that are relevant to the design and operation of PFVA-based systems. For each of them we (i) follow a first principles approach to develop a model, (ii) define dimensionless parameters and criteria that indicate the relative distribution of the quantity between the two inputs of the PFVA, (iii) express the basic model in terms of these dimensionless parameters, (iv) provide numerical examples using five candidate designs with commercial off-the-shelf components, (v) investigate the limiting case as the two inputs become more and more kinematically distinct, and (vi) suggest design guidelines based on our analysis. We studied four aspects of PFVA design: (i) mixing of position uncertainties of the two inputs, i.e., force actuator (FA) and velocity actuator (VA), (ii) distribution of static and inertia torques between the inputs for a given output loading condition, (iii) acceleration responsiveness, and lastly, (iv) effective stiffness of the PFVA system with respect to some basic design parameters of the PFVA. As an example result, we observed that the PFVA's effective stiffness will be at least 40% greater than that of the VA if the FA is 85% as efficient as the VA, the FA is 17% less stiff than the VA, and the kinematic scaling between the two inputs (FA and VA) is approximately 11.5. The results we obtained are organized into five design guidelines for the PFVA. To demonstrate the utility of this analysis and the guidelines, we present a design case study that describes a PFVA prototype. The results of this paper assist in better designing PFVA-based systems with a focus on the coupling between the two inputs.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Mechanisms Robotics. 2009;2(1):014501-014501-6. doi:10.1115/1.4000529.

Tristable mechanisms, or devices with three distinct stable equilibrium positions, have promise for future applications, but the complexities of the tristable behavior have made it difficult to identify configurations that can achieve tristable behavior while meeting practical stress and fabrication constraints. This paper describes a new tristable configuration that employs orthogonally oriented compliant mechanisms that result in tristable mechanics that are readily visualized. The functional principles are described and design models are derived. Feasibility is conclusively demonstrated by the successful operation of four embodiments covering a range of size regimes, materials, and fabrication processes. Tested devices include an in-plane tristable macroscale mechanism, a tristable lamina emergent mechanism, a tristable micromechanism made using a carbon nanotube-based fabrication process, and a polycrystalline silicon micromechanism.

Commentary by Dr. Valentin Fuster