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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.

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

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.

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.