Current design methods for flexure (or compliant) mechanisms regard stress as a secondary, limiting factor. This is remarkable because stress is also known as a useful design parameter. In this paper we propose the Stress And Geometry (STAGE) method, to design the geometry of a flexure mechanism together with a desired stress field. From this design, the stress-free to-be-fabricated geometry is computed using the inverse finite element method. To demonstrate the potential of the method, the geometry of the well-known crossed-flexure pivot is taken as example. We first show how this mechanism can be redesigned for the same functional geometry with various internal stresses. This results for a specific choice of stress field in a design of a crossed-flexure pivot with 23% lower peak stresses during motion as compared to the known designs, for a ±45° rotation. We then present a second example, of a Folded Leaf Spring (FLS). With a parameter sweep the optimal stress field is calculated, showing a peak stress reduction of 28% during motion. This result was validated with an experiment, showing a normalized mean absolute error of 5.5% between experiment and theory. With a second experiment it was verified that the functional geometry of the FLS with internal stresses was equal to the one without internal stresses, with geometric deviations smaller than half the thickness of the flexures.

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This paper investigates the possibilities for designing shaking force balanced spherical pantograph mechanisms. Three different spherical designs are presented, which are a balanced general spherical pantograph, a balanced double spherical pantograph and a double S-shaped mechanism with surrounding 4R four-bar linkage. Also variations of the balanced designs are presented. As compared to the planar balanced pantograph, the same underlying system of principal vectors exists, of which the geometries can be visualized in the orthogonal planes. The feasible variations of link lengths for which force balance is maintained are discussed.

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This paper proposes a design of a reconfigurable force balanced planar 4R four-bar linkage that can be applied for a variety of three-position motion tasks. Based on given and fixed link lengths of the four-bar linkage, from three-position synthesis the locations of the coupler pivots and base pivots can be derived for a desired set of three poses. With respect to the end-effector at the coupler link the two coupler pivots can be reconfigured in a balanced way with balanced five-bar parallelogram linkages such that force balance of the complete linkage is maintained at any time. Similarly the two base pivots can be reconfigured in a balanced way with balanced five-bar parallelogram linkages such that force balance of the complete mechanism is maintained for motion of the end-effector through any chosen set of three poses. The balance conditions for the complete mechanism are derived step by step with mass equivalent models.

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The acquisition of elemental and chemical distribution images on the surface of cultural heritage objects has provided us new insights into our past. The techniques commonly employed, such as macroscopic X-ray fluorescence imaging (MA-XRF), in general require pointwise or whisk-broom scanning of an object under constant measurement geometry for optimal results. Most scanners in this field use stacked linear motorized stages, which are a proven solution for 2D sample positioning. Instead of these serial systems, we propose the use of a parallel cable robot to position the measurement head relative to the object investigated. In this article, we illustrate the significance of the issue and present our own cable robot prototype and test its capabilities, but also discuss the current shortcomings of the concept. With this, we demonstrate the potential of cable robots as platforms for MA-XRF and similar imaging techniques.@en

Bicycle simulators have been the subject of considerable research, however, few of these attempts have integrated direct balance control and realistic freedom of motion to deliver a real-world dynamic cycling experience. This study presents the BIKE (Bicycle Intrinsic Kinematics Emulator) system, a kinematic bicycle simulator, developed with the purpose of letting its users experience realistic steer, roll, yaw and sway motions. Motion is provided with Carvallo–Whipple bicycle model-based control of sway and yaw combined with passive steer and roll. This study validates the BIKE simulator by comparing cycling behaviour and subjective evaluation for the simulator with and without motion to outdoor tests with an instrumented bicycle. 15 participants of varying age and mass, performed straight-line cycling, at low ((Formula presented.)) to high ((Formula presented.)) velocities and zig-zag manoeuvres. Results show that users can successfully rely on existing cycling skills to use the simulator with motion. Objectively, in the kinematic sense, the simulator with motion performs similarly to an outdoor bicycle. Subjectively, the simulator performs better with motion and is experienced by riders as close to real outdoor cycling.

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Humans vary the stiffness in their joints depending on tasks and circumstances. For posture control a high joint stiffness is required to withstand perturbations, whereas for force control a low joint stiffness is required. To investigate how humans vary their joint stiffness precisely for moving an arm, a wearable device is needed that can generate small force perturbations at the wrist while measuring the resulting muscular reactions. The majority of the state-of-the-art devices either offer too little versatility or impede the free movement of the arm. Based on a 3-DoF spatial redundant 4-RUU parallel manipulator applied in an inverted way where the original base with actuators has become the moving platform and the original moving platform is attached to the wrist as a bracelet, a versatile, 0.175 kg lightweight, low impedance, and compact wearable device was developed that can generate perturbation forces in X-, Y-, and Z-direction. The design and a prototype of the device are presented with experimental tests showing controlled perturbations in the order of 4 N with frequencies up to 12 Hz.

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This article presents the compliant manipulator design method (COMAD) for the synthesis of serial and parallel multi-DoF compliant mechanisms. Currently, the freedom and constraint topology (FACT)-method results in flexure systems being a serial kinematic solution for multi-DoF motions. In the COMAD method parallel solutions are included too through 3 steps: (1) obtaining the serial and parallel kinematic solutions for an intended set of end-effector DoFs with the type synthesis of legs-method; (2) transforming each legtype into a flexure leg by using the FACT method; (3) combining legs in parallel to obtain complete compliant mechanism designs. It was applied for a compliant Schönflies motion generator – having three translations and one rotation – resulting in 5 different 4-DoF flexure legs. 4 designs were new compared to the result obtained using the FACT method. Then, a set of legs was combined in parallel resulting in a compliant Schönflies mechanism, which was manufactured. Its mobility was experimentally evaluated by modal analysis. The intended motions separately became visible during its first four eigenmodes. They are the mechanism's DoFs as their stiffness is relatively low.

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Otto Fischer was during the late 19th and early 20th century the founder of 3-D human gait analysis. From motion recordings he calculated by hand the inverse dynamics of humans in motion, for which he discovered and used the principal vectors of a system of moving bodies. With the principal vectors the equations of motion and the kinetic energy can be written in a specific simple form with full geometric meaning and with reduced mass models with which system dynamics can be investigated in a simple way at link level. Fischer applied his theory mainly in its planar form. He also presented the theory of the spatial form by example of a serial two-link chain, however the explanations in the original texts in German are challenging to understand. This paper presents Fischer’s spatial form in a modern and understandable way.

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In this paper, we present the ADAPT, a novel reconfigurable force-balanced parallel manipulator for spatial motions and interaction capabilities underneath a drone. The reconfigurable aspect allows different motion-based 3-DoF operation modes like translational, rotational, planar, and so on, without the need for disassembly. For the purpose of this study, the manipulator is used in translation mode only. A kinematic model is developed and validated for the manipulator. The design and motion capabilities are also validated both by conducting dynamics simulations of a simplified model on MSC ADAMS, and experiments on the physical setup. The force-balanced nature of this novel design decouples the motion of the manipulator’s end-effector from the base, zeroing the reaction forces, making this design ideally suited for aerial manipulation applications, or generic floating-base applications.@en

The dynamic balancing of flexible mechanisms, that is, the reduction or elimination of shaking forces and shaking moments on the support structure, is considered. Two approaches are pursued: one uses similarity and the other modal balancing. A single rotating link can be balanced by a properly scaled countermass, for which balancing criteria are given. If all balancing conditions are satisfied, shaking force balance can even be achieved if geometric non-linearities are taken into account. This single link can be extended to a translator. Owing to the unscaled pitch of the translator and the asymmetric driving motor, no perfect shaking force balance is achieved, but the results can be considered satisfactory. Then, the dynamic balancing of a four-bar mechanism with a flexible coupler by means of modal balancing is shown. If the coupler is supported at the nodes of the first free vibration mode, this mode can be suppressed in the shaking force and shaking moment response. By supporting the coupler at four points with two whippletree mechanisms, the contribution of the first three symmetric vibration modes can be significantly reduced.

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This paper presents the spatial version of the well-known pantograph linkage. While the traditional pantograph is a planar parallelogram linkage with 1 internal degree of freedom (DoF) and four moving links connected with solely revolute pairs, the general spatial pantograph is a linkage with 3 internal DoFs in which the four moving links are connected with spherical joints and two additional out-of-plane links are connected with universal joints. The out-of-plane links constrain the linkage to maintain the essential parallelogram and also constrain all links to move similarly. This is necessary for full controllability and also for inherent force balance, which is obtained for specific conditions on the mass distribution of the links. The force balance conditions are given and also a reduced version of the spatial pantograph linkage with 2 internal DoFs is presented which has five moving links connected with solely universal joints.

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Compared to common dynamic balancing approaches, Inherent Dynamic Balancing aims at designing mechanisms with dynamic balance as a starting point. Then inherently balanced principal vector linkage architectures are used from which balanced linkage solutions are derived, ensuring the optimal kinematics for motions with a center of mass that is always stationary. This paper addresses various techniques for modifying principal vector linkage architectures in the synthesis process while maintaining the inherent balance. The techniques consist of constraining the mobility of links, shifting links to another position, and exchanging links with other machine elements such as sliders, gears, and belt and chain drives. To illustrate the potential, a synthesized 2-DoF inherently force balanced mechanism solution incorporating various techniques is presented and numerically evaluated for force balance.

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Industrial robotic manipulators in pick-and-place applications require short settling times to achieve high productivity. The fluctuating reaction forces and moments on the base of a dynamically unbalanced manipulator, however, cause base vibrations, leading to increased settling times. These base vibrations can be eliminated with dynamic balancing, which is achieved, in general, with the addition of counter-masses and counter-inertias. Adding these elements, however, comes at the cost of increased moving mass and inertia, resulting in lower natural frequencies and again higher settling times. For a minimal settling time it is therefore essential that a balanced mechanism has high natural frequencies with an optimal mass distribution. A dynamically balanced inverted four-bar linkage architecture is therefore favoured over architectures which depend on counter-masses and counter-rotating flywheels. The goal of this paper is to present and experimentally verify a structural design of a manipulator arm with high natural frequencies that is based on a dynamically balanced inverted four-bar linkage. The dynamical properties and the robustness to manufacturing tolerances are both verified with simulations and experiments. Experiments for 5.2 G tip accelerations show, when fully balanced, a reduction of 99.3% in reaction forces and 97.8% in reaction moments as compared to the unbalanced mechanism. The manipulator reached 21 G tip accelerations and a first natural frequency of 212 Hz was measured, which is significantly high and more than adequate for implementation in high acceleration applications. @en

In this paper it is shown how a 2-DoF inherently force balanced spatial deployable Butterfly Linkage is found consisting of four entangled similar Bennett linkages moving synchronously and with the common center of mass in the central joint. This linkage is derived from the Grand 4R Four-Bar Based Inherently Balanced Linkage Architecture by selecting a planar linkage with four entangled similar 4R four-bar linkages to which the Bennett conditions are applied. The inherent balance conditions are calculated, which are independent of the Bennett angles, and a CAD-model of the linkage is presented.

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In this paper we present two new designs of spherical flexure joints, which are the compliant equivalent of a traditional ball-and-socket joint. The designs are formed by tetrahedron-shaped elements, each composed of three blade flexures with a trapezoidal shape, that are connected in series without intermediate bodies. This is new with respect to the designs currently found in literature and helps to increase the range of motion. We also present two planar (x-y-θ_z) flexure joint designs which were derived as special versions of the spherical designs. In these designs the tetrahedron elements have degenerated to a triangular prisms. For detailed investigation we developed equivalent representations of the tetrahedron and triangular prism elements and proved that three of the four constraint stiffness terms depend solely on the properties of the main blade flexure. Furthermore, we derived equations for these stiffness terms which are compared to finite-element simulations, showing a good correspondence for the prism element with a Normalized Mean Absolute Error (NMAE) of 1.9%. For the tetrahedron element, the equations showed to only capture the qualitative behaviour with a NMAE of 34.9%. Also, we derived an equation for the optimal width of the prism element regarding rotational stiffness.

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Auxetic behavior refers to lateral widening upon stretching or, in reverse, lateral shrinking upon compression. When an initially auxetic structure is actuated by compression or extension, it will not necessarily remain auxetic for larger deformations. In this paper, we investigate the auxetic range in the deformation of a periodic framework with one degree of freedom. We use geometric criteria to identify the interval where the deformation is auxetic and validate these theoretical findings with compression experiments on sample structures with (Formula presented.) unit cells.

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In this paper, a pseudo-rigid body model is proposed for the analysis of a spatial mechanical metamaterial and its application is demonstrated. Using this model, the post-buckling behavior of the mechanical metamaterial can be determined without the need to consider the whole elastic structure, e.g., using finite-element procedures. This is done by analyzing a porous cylindrical mechanical metamaterial using a rigid body mechanism, consisting of rigid squares that are connected at their corners. Stiffness in this model comes from torsion springs placed at the connections between rigid parts. The theory of the model is presented and the results of two versions of this model are compared through experiments. One version describes the metamaterial in the free state, while the other, more extended, version includes clamped boundaries, matching the conditions of the experimental set-up. It is shown that the mechanical behavior of the spatial metamaterial is captured by the models and that the shape of the metamaterial in the deformed state can be obtained from the more extended model.@en

Considering balancing as starting point in the design of mechanisms and manipulators is known as inherent balancing. Inherently balanced linkage architectures then form the basis from which balanced mechanism solutions are synthesized, needing no countermasses contrary to balancing of given mechanisms. In this paper a new and advanced inherently balanced linkage architecture with the 4R four-bar linkage as a basis is presented, the Grand 4R Four-Bar Based Inherently Balanced Linkage Architecture. With 24 links it is 26 times overconstrained yet movable with stationary center of mass. It is shown that all theories for tracing the center of mass of a four-bar linkage are found inside. It is shown also how from this architecture a variety of new normally constrained 2-DoF balanced linkages are derived by removing a selection of links. This is done for the situations that all links are mass symmetric, for which 32 solutions are presented, and that all links have a general mass distribution. As an example, the balance conditions for the TWIN-4B, a solution of two similar 4R four-bar linkages, one inside the other, are derived and it is shown how this solution can be transformed into a spatial inherently balanced double Bennett linkage.

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The use of principal points and principal vectors in the formulation of the equations of motion of a general 4R planar four-bar linkage is shown with two kinds of methods, one that opens kinematic loops and one that does not. The opened kinematic loop approach analyses the moving links as a system with a tree connectivity, introducing reaction forces for closing the loops. Compared with the conventional Newton–Euler method, this approach results in fewer equations and constraint forces, whereas the mass matrix entries remain meaningful, but there is a stronger coupling between the equations. Two equivalent mass formulations for the closed kinematic loop approach are presented, which need not open the loop and introduce loop constraint forces in the equations of motion. With the method of complex joint masses, the mass of the links closing the loops is represented by real and virtual equivalent masses, defining the principal points. The principle of virtual work with the inclusion of inertia terms is used to derive the equations of motion. As an example the dynamic balance conditions of the four-bar linkage are derived. With the method of the equivalent mass matrix it is shown how a constant mass matrix can be used to describe the dynamics of binary links with an arbitrary mass distribution. A four-bar linkage could be modelled with only three truss elements instead of the conventional result with three or more beam elements, which gives a significant reduction of the computational complexity.

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This article presents a graphical analysis method for the verification of the gravity force balance and shaking force and shaking moment balance of a 1-DoF pantographic linkage. First the joint velocities of the linkage are graphically found of which the procedure is well known. To obtain the linear and angular momentum graphically, the mass and inertia of each element are modeled with two equivalent masses about the center of mass of the element, resulting in a mass and inertia equivalent model with solely point masses. The velocities of these point masses are obtained and each velocity vector is multiplied with the respective mass value to obtain vectors that represent the linear momentum. For force balance it is shown that the sum of all linear momentum vectors form a polygon. Subsequently the linear momentum vectors with their moment arms are transferred into an angular momentum diagram which for moment balance shows to sum up to zero.

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