Kinematic analysis of a single-loop reconfigurable 7R mechanism with multiple operation modes

This paper presents a novel one-degree-of-freedom (1-DOF) single-loop reconfigurable 7R mechanism with multiple operation modes (SLR7RMMOM), composed of seven revolute (R) joints, via adding a revolute joint to the overconstrained Sarrus linkage. The SLR7RMMOM can switch from one operation mode to another without disconnection and reassembly, and is a non-overconstrained mechanism. The algorithm for the inverse kinematics of the serial 6R mechanism using kinematic mapping is adopted to deal with the kinematic analysis of the SLR7RMMOM. First, a numerical method is applied and an example is given to show that there are 13 sets of solutions for the SLR7RMMOM, corresponding to each input angle. Among these solutions, nine sets are real solutions, which are verified using both a computer-aided design (CAD) model and a prototype of the mechanism. Then an algebraic approach is also used to analyse the mechanism and same results are obtained as the numerical one. It is shown from both numerical and algebraic approaches that the SLR7RMMOM has three operation modes: a translational mode and two 1-DOF planar modes. The transitional configurations among the three modes are also identified

Geometric constraints and motion branch variations for reconfiguration of single-loop linkages with mobility one

This paper explores essence of geometric constraints induced reconfiguration of single-loop kinematic chains with mobility one. Reconfigurable kinematic chains are firstly classified into four categories in light of variations of parameters in the Chebychev–Grübler–Kutzbach mobility criterion. Within these four categories, single-loop kinematic chains with mobility one but distinct motion branches are further classified in accordance with degeneration of degree-of-freedom of certain revolute joints. With the essence of reconfiguration, the interrelationship of motion-branch changes through constraint singularity induced transitory positions of reconfigurable single-loop linkages is revealed in the context of reciprocity of screws. Four basic geometric constraints leading to transitory positions are explored by analysing the Bennett plano-spherical linkage, a kinematic embodiment of Grassmann varieties. Geometric constraints induced screw-system variation and motion branch changes of a novel asymmetric 7R linkage and the line- and plane-symmetric Bricard 6R linkage with capability of reconfiguring their motion branches are subsequently analysed for interpreting the fundamentals explored

Reconfigurable mechanism generated from the network of Bennett linkages

A network of four Bennett linkages is proposed in this paper. Totally five types of overconstrained 5R and 6R linkages, including the generalized Goldberg 5R linkage, generalized variant of the L-shape Goldberg 6R linkage, Waldron's hybrid 6R linkage, isomerized case of the generalized L-shape Goldberg 6R linkage, and generalized Wohlhart's double-Goldberg 6R linkage, can be constructed by modifying this Bennett network. The 8R linkage formed by Bennett network serves as the basic mechanism to realise the reconfiguration among five types of overconstrained linkages by rigidifying some of the eight joints. The work also reveals the in-depth relationship among the Bennett-based linkages, which provides a substantial advancement in the design of reconfigurable mechanisms using overconstrained linkages

High-order based revelation of bifurcation of novel Schatz-inspired metamorphic mechanisms using screw theory

The revelation of mechanism bifurcation is essential in the design and analysis of reconfigurable mechanisms. The first- and second-order based methods have successfully revealed the bifurcation of mechanisms. However, they fail in the novel Schatz-inspired metamorphic mechanisms presented in this paper. Here, we present the third- and fourth-order based method for their bifurcation revelation using screw theory. Based on the constraint equations derived from the first- and second-order kinematics, only one linearly independent relationship between joint angular velocities at the singular configuration of the new mechanism can be generated, which means the bifurcation cannot be revealed in this way. Therefore, we calculate constraint equations from the third- and fourth-order kinematics, and attain two linearly independent relationships between joint angular accelerations at the same singular configuration that correspond to different curvatures of the kinematic curves of two motion branches in the configuration space. Moreover, motion branches in Schatz-inspired metamorphic mechanisms are demonstrated

Design of a compliant gripper with multimode jaws

This paper presents the design of a multimode compliant gripper, using the singularities of the four-bar mechanism with equilateral links. The mobility of the compliant gripper can be reconfigurable to grasp a variety of shapes or adapt to specific requirements. The compliant gripper is a compact and two-layer structure. Two linear actuators are required to enable the multiple operation modes, by the conversion of two pairs of slider-crank mechanisms. A multimode compliant four-bar mechanism is first presented and kinematically analyzed. The design and the kinetostatic modeling of the resulting compliant gripper are then performed. Finally, the analysis of the reconfigurable compliant gripper under different actuation schemes is carried out, including the comparison of the results obtained from analytical modeling, finite element analysis (FEA), and experimental testing

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

Position analysis based on multi-affine formulations

Aplicat embargament des de la data de defensa fins el 31/5/2022The position analysis problem is a fundamental issue that underlies many problems in Robotics such as the inverse kinematics of serial robots, the forward kinematics of parallel robots, the coordinated manipulation of objects, the generation of valid grasps, the constraint-based object positioning, the simultaneous localization and map building, and the analysis of complex deployable structures. It also arises in other fields, such as in computer aided design, when the location of objects in a design is given in terms of geometric constrains, or in the conformational analysis of biomolecules. The ubiquity of this problem, has motivated an intense quest for methods able of tackling it. Up to now, efficient algorithms for the general problem have remained elusive and they are only available for particular cases. Moreover, the complexity of the problem has typically led to methods difficult to be implemented. Position analysis can be decomposed into two equally important steps: obtaining a set of closure equations, and solving them. This thesis deals with both of them to obtain a general, simple, and yet efficient solution method that we call the trapezoid method. The first step is addressed relying on dual quaternions. Although it has not been properly highlighted in the past, the use of dual quaternions permits expressing the closure condition of a kinematic loop involving only lower pairs as a system of multi-affine equations. In this thesis, this property is leveraged to introduce an interval-based method specially tailored for solving multi-affine systems. The proposed method is objectively simpler (in the sense that it is easier to understand and to implement) than previous methods based on general techniques such as interval Newton methods, conversions to Bernstein basis, or linear relaxations. Moreover, it relies on two simple operations, namely, linear interpolations and projections on coordinate planes, which can be executed with a high performance. The result is a method that accurately and efficiently bounds the valid solutions of the problem at hand. To further improve the accuracy, we propose the use of redundant, multi affine equations that are derived from the minimal set of equations describing the problem. To improve the efficiency, we introduce a variable elimination methodology that preserves the multi-affinity of the system of equations. The generality and the performance of the proposed trapezoid method are extensively evaluated on different kind of mechanisms, including spherical mechanisms, generic 6R and 7R loops, over-constrained systems, and multi-loop mechanisms. The proposed method is, in all cases, significantly faster than state of the art alternatives.El problema de l'anàlisi de posició és un tema fonamental que subjau a molts problemes de la robòtica, com ara la cinemàtica inversa de robots sèrie, la cinemàtica directa de robots paral·lels, la manipulació coordinada d'objectes, la generació de prensions vàlides amb mans robòtiques, el posicionament d'objectes basat en restriccions, la localització i la creació de mapes de forma simultània, i l'anàlisi d'estructures desplegables complexes. També sorgeix en altres camps, com ara en el disseny assistit per ordinador, quan la ubicació dels objectes en un disseny es dóna en termes de restriccions geomètriques o en l'anàlisi conformacional de biomolècules. La omnipresència d'aquest problema ha motivat una intensa recerca de mètodes capaços d'afrontar-lo. Fins al moment, els algoritmes eficients per al problema general han estat esquius i només estan disponibles per a casos particulars. A més, la complexitat del problema normalment ha conduït a mètodes difícils d'implementar. L'anàlisi de posició es pot descompondre en dos passos igualment importants: l'obtenció d'un sistema d'equacions de tancament i la resolució d'aquest sistema. Aquesta tesi tracta de tots dos passos per tal d'obtenir un mètode de solució general, senzill i alhora eficient que anomenem el mètode del trapezoide. El primer pas s'aborda utilitzant quaternions duals. Tot i que no ha estat suficientment destacat en el passat, l'ús de quaternions duals permet expressar la condició de tancament d'un bucle cinemàtic que impliqui només parells inferiors com a un sistema d'equacions multi-afins. En aquesta tesi s'aprofita aquesta propietat per introduir un mètode especialment dissenyat per resoldre sistemes multi-afins. El mètode proposat és objectivament més senzill (en el sentit que és més fàcil d'entendre i d'implementar) que els mètodes anteriors que utilitzen tècniques generals com ara els mètodes de Newton basats en intervals, les conversions a la base de Bernstein o les relaxacions lineals. A més, el mètode es basa en dues operacions simples, a saber, les interpolacions lineals i les projeccions en plans de coordenades, que es poden executar de forma molt eficient. El resultat és un mètode que acota amb precisió i eficiència les solucions vàlides del problema. Per millorar encara més la precisió, proposem l'ús d'equacions multi-afins redundants derivades del conjunt mínim d'equacions que descriuen el problema. Per altra banda, per millorar l'eficiència, introduïm un metodologia d'eliminació de variables que preserva la multi-afinitat del sistema d'equacions. La generalitat i el rendiment del mètode del trapezoide s'avalua extensivament en diferents tipus de mecanismes, inclosos els mecanismes esfèrics, bucles 6R i 7R genèrics, sistemes sobre-restringits i mecanismes de múltiples bucles. El mètode proposat és, en tots els casos, significativament més ràpid que els mètodes alternatius descrits en la literatura fins al moment.Postprint (published version

Reconfiguration analysis of a 3-DOF parallel mechanism

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel manipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed of a base and a moving platform shaped as equilateral triangles connected by three serial kinematic chains (legs). Two legs are composed of two universal (U) joints connected by a prismatic (P) joint. The third leg is composed of a revolute (R) joint connected to the base, a prismatic joint and universal joint in sequence. A set of constraint equations of the 1-RPU−2-UPU PM is derived and solved in terms of the Euler parameter quaternion (a.k.a. Euler-Rodrigues quaternion) representing the orientation of the moving platform and of the Cartesian coordinates of the reference point on the moving platform. It is found that the PM may undergo either the 3-DOF PPR or the 3-DOF planar operation mode only when the base and the moving platform are identical. The transition configuration between the operation modes is also identified

Assembly of reconfigurable Bricard-like mechanisms to form a multimode deployable arch

This paper deals with the construction of a novel family of multimode deployable mechanisms based on reconfigurable Bricard-like mechanisms. By connecting a number of identical threefold-symmetric (TFS) Bricard-like mechanisms, a multimode deployable arch is proposed for the first time, which can switch between the scissor-like deployable mode and the arch deformable mode through the transition configuration. Then new multimode center-driven deployable mechanisms can be obtained by connecting three and six multimode deployable arches. The obtained mechanism can switch between the scissor-like deployable mode and spherical deformable mode, and it can be reassembled by adjusting the number of TFS Bricard-like mechanisms to change its size. Finally, physical prototypes of the multimode deployable arch and multimode center-driven deployable mechanisms are fabricated and tested to validate the feasibility of the proposed approach and analysis.</p