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. -------------------------------------------------------------------------------

Type synthesis and static balancing of a class of deployable mechanisms

This thesis addresses the type synthesis and static balancing of a class of deployable mechanisms, which can be applied in applications in many areas including aerospace and daily life. Novel construction methods are proposed to obtain the deployable mechanisms. First, the type synthesis of the foldable 8-revolute joint (R) linkages with multiple modes is presented. Two types of linkages are constructed by connecting planar 4R linkages and spherical 4R linkages. The obtained linkages can be folded into two layers or four layers, and have multiple motion modes. A spatial triad is also adopted to build single-loop linkages, then the single-loop linkages are connected using spherical (S) joints or RRR chains to obtain deployable polyhedral mechanisms (DPMs). The DPMs have only 1- degree-of-freedom (DOF) when deployed, and several mechanisms with 8R linkages and 10R linkages have multiple motion modes and can switch modes through transition positions. In addition, when connecting single-loop linkages using half the number of the RRR chains, the prism mechanisms obtain an additional 1-DOF rotation mode. Furthermore, the DPMs are developed into statically balanced mechanisms. The geometric static balancing approaches for the planar 4R parallelogram linkages, planar manipulators, spherical manipulators and spatial manipulators are developed so that the mechanisms can counter gravity while maintaining the positions of the mechanisms. Only springs are used to design the statically balanced system readily, with almost no calculation. A novel numerical optimization approach is also introduced which adopts the sum of squared differences of the potential energies as the objective function. Using the proposed static balancing approaches, the 8R linkages and the DPMs presented in this thesis can be statically balanced

Sliceforms: Deployable structures from interlocking slices

A sliceform is a volumetric, honeycomb-like structure assembled from an array of cross-sectional planar slices that are interlocked via pairs of complementary slots placed along each intersection. If the slices are thin, these slotted intersections function as revolute joints, and the sliceform is foldable if the geometry of the embedded spatial linkage permits it, for example a lattice sliceform (LS) is bi-directionally flat-foldable. This thesis concerns a study of such sliceforms toward the design of novel deployable structures. A sliceform torus, composed of two sets of inclined slices arranged at regular intervals about a central axis of symmetry, has been discovered to exhibit a surprising and intriguing folding action whereby its incomplete form can be collapsed to a flat-folded stack of coplanar slices. On deployment, the assembly expands smoothly about an arc until the slices have rotated to their design inclination, then, without reaching any apparent physical limit, abruptly ‘locks out’. With a full complement of slices, the outermost intersections can be interlocked to complete and rigidify the ring. The torus is an example of a rotational sliceform (RS), and analysis of these structures proceeds by noting that their structural geometry comprises an array of pyramidal cells that is commensurate to a spherical scissor grid. The conditions for flat-foldability are determined by examination of the intrinsic geometry of each cell; the incompatibility of the slices with apparent rigid-folding revealed by assessment of the extrinsic motion of the slices. Investigation of their compliant kinematics reveals the articulation to be a bistable transition admitted by small transverse deflections of the slices. This structural form is generalised by development of a technique for generating sliceforms along a smooth spatial curve – curve sliceforms (CS). Their synthesis is more involved than for an RS, but a range of sliceform ‘tubes’ are generated and manufactured. Each example retains the flat-foldable, deployable characteristic of an RS, despite the apparent intrinsic rigidity of each constituent skew cell. Examination of the small-scale models indicates that deployable motion is achieved via imperfect action of the slots, and a simple model of the articulation of a single cell is constructed to investigate how this proceeds, verifying that motion is kinematically admissible via local deformations

A power system simulator for transient stability studies

Imperial Users onl