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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.

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.

Cultural heritage science envisages understanding of methods and techniques used by past painters and sculptors in creating their masterpieces of art. Existing devices for in situ and non-destructive, automated scanning are large and bulky and built around the assumption of a perfectly planar surface. We are developing a lightweight, portable robot for scanning of paintings, marbles, or statues while explicitly allowing for their out-of-plane surface. This paper presents the kinematic design and analysis of the wrench-feasible workspace of a cable-driven parallel robot capable of positioning an imaging device with three translational and two rotational degrees of freedom. At the end stand geometric parameters optimized for the application requirements allowing for pan and tilt of 70\(^{\circ }\) each in total, making scanning of the spatial surface of art objects possible.

A reconfigurable mechanism can be defined as a mechanism with changingmobility due to its specific mechanical design, for example changing from aconfiguration with one degree of freedom to a configuration with two degreesof freedom motion. Due to the practical and theoretical challenges of developinga reconfigurable mechanism and also because of the high variety of designpossibilities, this topic pushes the designer to employ all of his or her creativity.

Dilational structures are one degree of freedom structures able to change their size without changing their global shape. In this paper, we present a method to create dilational shells with arbitrary curvature. For this, we designed triangular tiles, which can be placed on a triangulation of the desired surface. We present the method and illustrate it with the example of a dilational octahedron. Using this regular polygon, we demonstrate that the whole structure has a single degree of freedom, and that the maximum obtainable scaling factor is directly linked to the range of motion of the individual triangular tiles.

Force balance is an important feature in high-speed machinery to move fast without base vibrations and in large moving structures to move safely and with minimal effort. Advantageous balanced linkages can be synthesized from inherently balanced linkage architectures, i.e. linkages with solely the essential kinematic relations for balance. The center of mass of such a linkage is in a stationary point in one of the links for all motion. In this paper it is shown that the known 4R four-bar based inherently balanced linkage architecture is only part of the complete or grand 4R four-bar based inherently balanced linkage architecture, which is presented here. It is shown that this architecture comprises all related theories and that they all depend on principal vectors. Also various new balanced linkages are derived.

Force balance is an important property in the design of high-speed high precision machinery to reduce base vibrations and also for the design of inherently safe large movable structures. This paper presents the synthesis of inherently balanced overconstrained focal mechanisms with mass equivalent pantographs. It is shown how pantograph linkages can be combined into an overconstrained but movable linkage by connecting them in their similarity points. With mass equivalent modeling the force balance conditions are derived for which the common center of mass is in the focal point for any motion. As examples Burmester’s focal mechanism is investigated for balance and a new balanced focal mechanism of three mass equivalent pantographs is presented.

In this paper it is shown how a general 3-DoF triad can be designed mass equivalent to a general (1-DoF) link element. This is useful in the synthesis of shaking force balanced and statically balanced mechanisms, for instance to add or remove a number of DoFs of a balanced mechanism maintaining its balance. Also it can be used as a simple approach for synthesis of complex balanced mechanisms. To obtain the parameters for mass equivalence, a mass equivalent model with real and virtual equivalent masses is used. The characteristics of this model are explained and the properties of a mass equivalent triad are shown. Subsequently the parameters of a mass equivalent triad are derived with the method of rotations about the principal points (RAPP) and application examples are il-lustrated and discussed.

This paper shows how umbrella canopies and umbrella canopy-like mechanisms can be designed inherently balanced. Inherently balanced means that the center of mass of the moving parts remains stationary at a single point for any position of the mechanism simply because of the specific design of the mechanism where no countermasses or springs are needed. The advantages of a balanced canopy are that it can be opened and closed easily with minimal effort even if it has large dimensions and that it is inherently safe since the canvas cannot collapse or fall down. Also a shaking ground or floor does not affect an inherently balanced canopy. This is due to its dynamic force balance, allowing the canopy to be perfectly suitable as a retractable roof on for instance a truck on a bumpy road. In this study, three inherently balanced umbrella canopy designs are synthesized from principal vector linkages and their balance conditions are derived. Also a prototype was built and tested to show the feasibility of the design in practice.

In this paper it is shown how a general 2-DoF dyad can be designed mass equivalent to a general (1-DoF) link element. This is useful in the synthesis of balanced mechanisms, for instance to increase or reduce the number of DoFs of a balanced mechanism maintaining its balance. Also it can be used as a simple approach for synthesis of complex balanced mechanisms. For finding the parameters for mass equivalence, a mass equivalent model with real and virtual equivalent masses is used. First the characteristics of this model are explained, then the properties of a mass equivalent dyad are shown. Subsequently with two methods the parameters of a mass equivalent dyad are derived and application examples are illustrated and discussed.

For high-speed robotics dynamic balance is an important property for low base vibrations and short cycle times. To consider dynamic balance in the beginning of the design process of a manipulator, mechanism solutions can be synthesized from principal vector linkages, which are fundamental kinematic architectures with inherent force balance. In this paper it is shown how a closed-chain principal vector linkage can be analyzed as an open-chain principal vector linkage by modeling one element in a closed chain with two real and two virtual equivalent masses. The results are validated with a dynamic simulation.

A mechanism or robotic manipulator that is dynamically balanced does not cause base vibrations when moving at high speeds. A balanced mechanism does not perturb equipment mounted on the same base, the floor, and machines placed nearby, therefore dynamic balance improves the accuracy of a machine, reduces cycle times, and reduces the required size, mass, and stiffness of base frames and floors. For robotic end-effectors dynamic balance is advantageous because of dynamic decoupling. A balanced mechanism also remains stationary in any position which is advantageous for realizing safe and energy efficient large motion of objects. Since commonly dynamic balancing of multi-degree-of-freedom mechanisms is considered after the kinematic synthesis of a mechanism, profitable solutions without excessive mass, inertia, and complexity addition are hardly found. In this work a methodology was developed that considers dynamic balance as a design principle in the synthesis of dynamically balanced mechanisms. New mechanisms were found where all elements contribute to the motion as well as to the dynamic balance. Such mechanisms were named inherently dynamically balanced mechanisms. Two methods for the synthesis of inherently dynamically balanced mechanisms were proposed which consider dynamic balance prior to the kinematic synthesis, the ‘method of linearly independent linear momentum’ and the ‘method of principal vector linkages’. Also a method was found by which the loop closure relations of general planar closed kinematic chains can be considered implicitly. For that purpose the mass of an element with general center-of-mass is modeled with one virtual equivalent mass and two real equivalent masses. For the first time a high-speed inherently dynamically balanced parallel manipulator was designed, built, and tested, showing that with dynamic balance the performance of the manipulator can be improved significantly. New multi-degree-of-freedom balanced kinematic mechanism solutions were synthesized for various applications such as a balanced grasper, a balanced bascule bridge without counter-mass, and balanced movable architecture.

Shaking forces and shaking moments in high-speed machines and manipulators are a significant cause of base vibrations. These vibrations can be eliminated by designing the manipulator to be shaking-force balanced and shaking-moment balanced, or in short: dynamically balanced. The design and experimental results of a high-speed dynamically balanced parallel manipulator are presented, showing the potential of dynamic balance for machine design

The design of shaking-force balanced linkages can be approached by deriving these linkages from balanced linkage architectures. When desired, a possible step is to add degrees-of-freedom (dof), for instance by substituting a link with a n-dof equivalent linkage for which the balanced design of the other links is not affected. This paper shows how the coupler link of a shaking-force balanced 4R four-bar linkage, applied as a 5R five-bar linkage, can be substituted with an equivalent 2-dof pantograph.

The design of shaking-moment-balanced linkages still is challenging. Considering moment balance in the very beginning of the design process of mechanisms is important for finding applicable solutions. For this purpose, the method of principal vectors is investigated, showing a compact notation of the angular momentum with respect to the center of mass. The moment-balance conditions are derived for three links in series from which balance solutions are synthesized and illustrated. The application for moment balancing of a 4R four-bar linkage is shown.

In this paper, a device based upon a specific cable-driven parallel mechanism to interact with hemispherical surfaces is proposed and investigated. This device could be of use in, for example, the automated cleaning of glass domes. Because the cables move on the hemispherical surface, they are curved. A method is developed to calculate the inverse kinematics and the workspace of this mechanism. This method and device are applied to and evaluated for an example of a large glass dome, showing its potential for this purpose.

In this paper, the capability of a specific cable-driven parallel mechanism to interact with a variety of surfaces is investigated. This capability could be of use in for example the cleaning of large building surfaces. A method is presented to investigate the workspace for which the cables do not interfere and a surface interaction force can be generated. This method takes into account the influence of cable mass. As an example, this method is used for the design of a mechanism with a workspace conform to the dimensions of a typical building facade. The mechanism is concluded to be feasible as long as there is room to locate the pulleys at an adequate distance from the surface.

Synthesis of mechanisms with their center of mass (CoM) at an invariant point on one of the elements is useful for the design of statically balanced and shaking-force balanced mechanisms and manipulators. For this purpose, a kinematic architecture based on a general 4R four-bar linkage is found by applying the method of principal vectors as a linkage together with a similar four-bar linkage. The balance conditions are obtained for an arbitrary mass distribution of each of the elements and a balanced grasper mechanism and a balanced two-degree-of-freedom manipulator are derived as practical examples

This article gives an overview of the distinctive work of Otto Fischer (1861-1916) on the motion of the human musculoskeletal system. In order to be able to derive the individual muscle forces for human in motion, he invented the method of principal vectors to describe the motion of the centers-of-mass and the inertias of body segments. This method has proven to be successful, not only for the studies on biomechanics but in particular also for mechanism and machine science. A historical development of the application of the method is presented for today’s potential.

The invention relates to a delta robot comprising a stationary base (2) and a movable platform (3) that is connected to the base with three chains of links (4,5,6), and comprising a balancing system incorporating at least one pantograph (7) for balancing the robot's center of mass, wherein the at least one pantograph has a first free extremity (10) at which it supports a countermass (13) which is arranged to balance the center of mass of the robot.

Een dynamisch gebalanceerde robot beweegt zonder trillingen te veroorzaken in de basis. Hierdoor kan hij met hogere precisie en kortere omlooptijden werken. Actief dynamisch balanceren maakt het mogelijk om relatief eenvoudig en met weinig toegevoegde massa complexe robotica te balanceren, inclusief de payload

This article presents a systematic investigation of the dynamic balancing of a singlecrank-double slider mechanism of which the coupler links have symmetric motion. From the equationsof the linear momentum and angular momentum the force balance conditions and momentbalance conditions are derived. Both general and specific force balanced and moment balancedconfigurations are obtained step by step, are put in perspective, and are illustrated to gain a systematicoverview of the balancing possibilities of this type of mechanism. Also the addition of acounter-rotating element is considered

Dynamic balance of machines is important when, for example, high precision in combination with low cycle times is necessary. One of the major problems with dynamic balancing is that considerable mass and considerable inertia need to be added to the mechanism. So far, only a few studies have been carried out into the comparison of various dynamic balancing principles in order to reduce these additions. Based on the findings of these studies, this paper aims to formulate guidelines for the design of dynamically balanced mechanisms with low mass and low inertia additions. Furthermore, the influence of limited design space on the resulting mass and inertia is investigated

The Delta robot has shown to be a useful device in many applications. Due to large accelerations however, vibrations can decrease the accuracy and performance considerably. Instead of common techniques to reduce vibrations such as damping or including waiting times in the motion cycle, this article shows how the Delta robot can be dynamically balanced in a practical way by which all vibrations are eliminated. Because of its specific architecture, the Delta robot can be force balanced with only three counter-masses and two additional links. Moment balancing can be achieved by active actuation of three additional rotating inertias

When dynamically balanced mechanisms and robots are used for pick and place motion, the payload influences the dynamic balance. The payload can be a cause of serious vibrations which for instance can reduce the accuracy of the mechanism considerably. In such a case reconfiguration of the mechanism during pick and place motion can help correct the dynamic balance. Due to rapid motion and short cycle times however, the reconfiguration has to be done rapidly and can be a cause of serious vibrations in itself. To eliminate these vibrations, the reconfiguration should preferably be done in a dynamically balanced way. Since moment balancing can conveniently be done actively in any situation, this article focusses on force-balanced reconfiguration of mechanisms to force balance variable payload. Three fundamental approaches to force-balanced reconfiguration were obtained: (1) reconfiguration by relocating the balancing mass, (2) reconfiguration by relocating the center-of-rotation of the link with balancing mass and (3) reconfiguration by changing the value of the balancing mass. It is shown that under certain circumstances a mechanism with payload can be force balanced by force-balanced reconfiguration. In addition, all approaches can be applied to either obtain partial force-balance of the mechanism with payload in a perfectly force-balanced way, or to obtain perfect force balance of the mechanism with payload in a partially force-balanced way, i.e. for which the vibrations during reconfiguration are reduced.

Most materials around us have properties that are determined at extremely small scales. Often the atoms and molecules that make up these materials determine how they behave under load. While this already leads to a great variety of material properties, a lot more is possible. Mechanical metamaterials use structure to extend the available range of material properties. In this way, we can design material properties that are not found in nature. An example of this is materials with a negative Poisson’s ratio. When these materials are compressed, they will not expand in the direction perpendicular to the applied deformation, as we would expect from natural materials. Rather, they will contract.In general, mechanical metamaterials allow us to design materials with properties that are tailored to their intended solution. This provides more design freedom; instead of choosing from a list of available materials, the material properties themselves now become variables that can be designed. Additionally, this makes it possible to integrate multiple functions within a material. In this way, the material is no longer passive but can react based on applied forces, deformations, or changes in the environment. In practice, designing mechanical metamaterials has turned out to be difficult. While there are many examples of mechanical metamaterials with exceptional properties, their discovery has rarely been based on a rational and structured design process. The lack of such a design strategy makes the design of metamaterials with exactly the desired properties, at least for now, difficult and unreliable.This dissertation explores this design problem and presents a method to aid in the structured and rational design of mechanical metamaterials. This method is based on a pseudo-rigid body approach, borrowed from the field of compliant mechanisms. Following this approach, the metamaterial is modeled as a collection of rigid parts, which are connected by joints to which we assign a stiffness. This allows us to model both the deformation and the stiffness of the material while keeping the complexity of the models as low as possible.Because of the limited complexity of the models, this approach allows the designer to understand the effects of design decisions and adaptations. This enables directed and conscious changes to the design, of which the consequences are known beforehand. This is different from alternative methods where highly complex and time-consuming computer models are used to calculate the effects of changes. By using less complex models and making directed choices, new design iterations can be generated more quickly. Especially at the start of a design process, this is expected to quickly lead to new insights. These can then at a later stadium be refined using more detailed methods.