On the addition of degrees of freedom to force-balanced linkages

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

Mass equivalent triads

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

Synthesis method for linkages with conter of mass at invariant link point-Pantograph based mechnisms

This paper deals with the synthesis of the motion of the center of mass (CoM) of linkages as being a stationary or invariant point at one of its links. This is of importance for the design of inherently shaking force balanced mechanisms, static balancing, and other branches of mechanical synthesis. For this purpose Fischer's mechanism is investigated as being a composition of pantographs. It can be shown that linkages that are composed of pantographs and of which all links have an arbitrary CoM can be inherently balanced for which Fischer's method is a useful tool. To calculate the principal dimensions for which linkages have their CoM at an invariant link point, an approach based on linear momentum is proposed. With this approach it is possible to investigate each degree-of-freedom individually. Equivalent Linear Momentum Systems are proposed to facilitate the calculations in order to use different convenient reference frames. The method is applied to planar linkages with revolute joints, however it also applies to linkages with other types of joints. As a practical example a shaking force and shaking moment balanced 2-DoF grasper mechanism is derived. -------------------------------------------------------------------------------

Synthesis and Experiments of Inherently Balanced Umbrella Canopy Designs

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

Generic method for deriving the general shaking force balance conditions of parallel manipulators with application to a redundant planar 4-RRR parallel manipulator

This paper proposes a generic method for deriving\ud the general shaking force balance conditions of parallel\ud manipulators. Instead of considering the balancing of a parallel\ud manipulator link-by-link or leg-by-leg, the architecture is\ud considered altogether.\ud The first step is to write the linear momentum of each element.\ud The second step is to substitute the derivatives of the\ud loop equations, by which the general force balance conditions\ud are obtained. Subsequently specific kinematic conditions are\ud investigated in order to find advantageous, simple balance solutions.\ud As an example, the method is applied to a planar 4-RRR parallel\ud manipulator, for which the force balance conditions and\ud solutions are discussed and illustrated for each step respectively.\ud By including the loop equations, linear relations of the\ud motion among mechanism elements lead to an increase of balance\ud possibilities.For specific kinematic conditions, additional\ud linear relations among the motion of mechanism elements may\ud be obtained, resulting in another increase of balance possibilities.\ud For the latter, symmetric motion is an important feature\ud for which a 4-RRR manipulator is advantageou