Spherical Mechanism Research Articles

A Novel Hydraulic Spherical Joint and Motion Analysis

Proposing a new type of hydraulic drive spherical joint with two degrees of freedom.The joint mechanism has the advantages of hydraulic and also can rotate with multi-degrees of freedom. Based on the mechanism theory, the forward and inverse kinematics equations are derivated and the singular configuration and workspace of the mechanism are found. The spherical joint mechanism has these characteristics: a compact structure, low coupling, large load, and the joint can complete the omni-directional output.

Kinematic Transmission Analysis of a Novel Spherical 3-RRR Parallel Manipulator

The kinematic transmission property and distributions in workspace of a novel spherical 3-RRR parallel mechanism are given. The orthogonal layout feature of the parallel mechanism is described. The equations for inverse displacement and kinematic transmission property are derived by the relation of geometry. The kinematic transmission evaluation index of a spherical 3-RRR parallel mechanism is defined. Finally, the distribution of the index in workspace was given, which can provide theoretical basis for the application of the spherical mechanism.

Error Analysis of a Manipulators

The forearm is a typical ball and socket joint which have three degrees of freedom rotation. In this case the study of a 3-DOF manipulators is very interesting. In this paper, a novel manipulators based on 3-DOF orthogonal spherical parallel mechanism is proposed. Error analysis play an important role on the design and applications of the manipulators. The error model is derived in closed forms by using differential theory. Error evaluation index is defined. Terminal platform error distribution is analyzed and discussed in detail by using the error model technique. The analytic results indicate error value is smallest in initial position of the manipulators,the bigger value of error distributes in the workspace edge. So, this paper could provide a theoretical foundation for design and application of the manipulators.

Design and experiment of a compact wrist mechanism with high torque density

This paper proposes a new wrist mechanism for robot manipulation. To develop multi-DOF wrist mechanisms that can emulate human wrists, compactness and high torque density are the major challenges. Traditional approaches use a series of rotary motors that require gearing to amplify the output torque. This often results in an oversized wrist. Alternatively, large linear force can be easily attained in a compact space by using leadscrew motors. Inspired by the muscle–tendon actuation pattern, the proposed mechanism consists of two parallel placed linear motors. Their translational motions are transmitted to two perpendicular axes of rotation through a spherical mechanism and two slider crank mechanisms. A high torque density can be achieved. Static and dynamic models are developed to design and analyze the wrist mechanism. Experiments of a wrist prototype are presented and the results are discussed. The novel mechanism is lightweight and has a humanlike appearance. It is expected to serve as a basis to develop humanoid manipulators for human-friendly interactions.

Variable step-size numerical atlas method for path generation of spherical four-bar crank-slider mechanism

This paper presents a new method for the path generation of spherical four-bar crank-slider mechanism. Based on the established mathematical model of the spherical four-bar crank-slider mechanism, the expression of the coupler curve is determined. Then, depending on Fourier series theory, the immanent connection between coupler curve and its corresponding harmonic characteristic parameters is discovered. Meanwhile, by the analysis of the basic dimensional type and the coupler curve, different step size for each parameter of the basic dimensional type is chosen. Thus, by putting the harmonic characteristic components and associated basic dimensional type of spherical four-bar crank-slider mechanism together, a variable step size numerical atlas database of the spherical four-bar crank-slider mechanism is created. Furthermore, by using fuzzy identification method, the best suitable basic dimensional type of spherical four-bar crank-slider mechanism for prescribed coupler curve is obtained. Finally, an example is given to illustrate the synthesis process and the application of this method.

A position analysis of coupled spherical mechanisms found in action origami

Origami has been previously utilized in design to create deployable systems. Action origami, origami designed to move, has the ability to deploy to a larger state and have motion in the deployed state. The majority of action origami achieves motion through coupled systems of spherical mechanisms. An origami vertex, the point at which folds converge, is shown to be equivalent to a spherical change-point mechanism. A position analysis of an origami vertex is presented, resulting in a relationship between input and output angles as well as the path of the coupler link. A method for analyzing coupled systems of repeated spherical mechanisms is proposed and demonstrated using two examples. A better understanding of the kinematics of action origami increases the ability of designers to create compact, deployable mechanisms for use in packaging, space, and medical industries.

Design and kinematic analysis of redundantly actuated parallel mechanisms for ankle rehabilitation

SUMMARYIn this paper, we present the design of two serial spherical mechanisms to substitute for a single spherical joint that is usually used to connect the platform with the base in three degrees of freedom parallel mechanisms. According to the principle derived from the conceptual design, through using the two serial spherical mechanisms as the constraint limb, several redundantly actuated parallel mechanisms are proposed for ankle rehabilitation. The proposed parallel mechanisms all can perform the rotational movements of the ankle in three directions while at the same time the mechanism center of rotations can match the ankle axes of rotations compared with other multi-degree-of-freedom devices, due to the structural characteristics of the special constraint limb and platform. Two special parallel mechanisms are selected to analyze their kinematical performances, such as workspace, dexterity, singularity, and stiffness, based on the computed Jacobian. The results show that the proposed scheme of actuator redundancy can guarantee that the redundantly actuated parallel mechanisms have no singularity, better dexterity, and stiffness within the prescribed workspace in comparison with the corresponding non-redundant parallel mechanisms. In addition, the proposed mechanisms possess certain reconfigurable capacity based on control strategies or rehabilitation modes to obtain sound performance for completing ankle rehabilitation exercise.

On the location of the secondary instantaneous poles in two-degree-of-freedom spherical mechanisms

As the instant centers in planar mechanisms, the instantaneous poles (or instant poles, in brief) can be used for kinematic analysis in spherical mechanisms. One of the mandatory steps in this analysis is the determination of the location of these poles. This paper presents a theorem showing analytically that the locus of an unknown secondary instant pole in two-degree-of-freedom (2-DOF) spherical mechanisms is a great circle (GC). The exact location of the pole on its GC is obtained based on the configuration of the mechanism and velocity ratio of the two inputs. Moreover, using the results of the theorem, a geometrical technique is presented to determine the GC of the pole.

One-degree-of-freedom spherical model for the passive motion of the human ankle joint

Mathematical modelling of mobility at the human ankle joint is essential for prosthetics and orthotic design. The scope of this study is to show that the ankle joint passive motion can be represented by a one-degree-of-freedom spherical motion. Moreover, this motion is modelled by a one-degree-of-freedom spherical parallel mechanism model, and the optimal pivot-point position is determined. Passive motion and anatomical data were taken from in vitro experiments in nine lower limb specimens. For each of these, a spherical mechanism, including the tibiofibular and talocalcaneal segments connected by a spherical pair and by the calcaneofibular and tibiocalcaneal ligament links, was defined from the corresponding experimental kinematics and geometry. An iterative procedure was used to optimize the geometry of the model, able to predict original experimental motion. The results of the simulations showed a good replication of the original natural motion, despite the numerous model assumptions and simplifications, with mean differences between experiments and predictions smaller than 1.3mm (average 0.33mm) for the three joint position components and smaller than 0.7° (average 0.32°) for the two out-of-sagittal plane rotations, once plotted versus the full flexion arc. The relevant pivot-point position after model optimization was found within the tibial mortise, but not exactly in a central location. The present combined experimental and modelling analysis of passive motion at the human ankle joint shows that a one degree-of-freedom spherical mechanism predicts well what is observed in real joints, although its computational complexity is comparable to the standard hinge joint model.

Parallel singularity-free design with actuation redundancy: A case study of three different types of 3-degree-of-freedom parallel mechanisms with redundant actuation

Typical parallel mechanisms suffer from parallel singularity due to kinematic coupling of multichains. This paper investigates how to remove parallel singularities by using redundant actuations. First, actuation wrenches and constraint wrenches forming the full direct kinematic Jacobian matrix are derived. After briefly addressing conditions for their constraint singularities, Grassmann–Cayley algebra is employed to identify parallel singularities. Then, employing Grassmann line geometry, the locations and the minimum number of redundant actuators are identified for the parallel mechanisms to have parallel singularity-free workspace. Three different types of 3-degree-of-freedom parallel mechanisms such as planar, spherical, and spatial parallel mechanisms are given as exemplary devices.

A Classification of Action Origami as Systems of Spherical Mechanisms

Action origami is a field of origami dealing with models that are folded so that in their final, deployed state they exhibit motion. Hundreds of action origami models exist, many of which use complicated kinematics to achieve motion in their deployed state. A better understanding of the mechanisms used to create motion in action origami could be a foundation for developing a new source of concepts for deployable, movable engineering solutions. This brief presents an approach for evaluating and classifying the mechanisms that enable action origami motion. Approximately 130 action origami models are investigated. Although disguised with artistic elements, it is found that most action origami models are based on a few fundamental mechanisms. A classification scheme is proposed, and an unexplored class of action origami is identified as an area for future origami art.

Synthesis of adjustable spherical four-link mechanisms for approximate multi-path generation

An optimization based method is presented for the synthesis of adjustable spherical four-link crank–rocker mechanisms for approximate multi-path generation. The synthesis is done in two stages, first the driving dyad of the spherical mechanism is determined and then the remaining parameters are determined. The method uses a least squares based plane fitting procedure and this results in a lesser number of design variables for optimization than existing approaches. Two numerical examples, including one dealing with generating two different trajectories of a flapping wing micro air vehicle, are presented to demonstrate the effectiveness of the proposed synthesis method.

Kinematics Analysis of a 3-RRR Spherical Parallel Mechanism with Coaxial Input Shafts

As an important mechanism with special and extensive application, the three degrees of freedom spherical parallel mechanism is always a research hot in the mechanical fields. In this paper, the feature of the 3-RRR spherical parallel mechanism with coaxial input shafts is introduced, and its motion feature is analyzed based on the screw theory. The mobility of the spherical parallel mechanism is calculated by using the Modified Kutzbach-Grübler criterion, and the inverse displacement problem of the mechanism is solved. Then the expression of the Jacobian matrix is deduced based on the kinematics equation and its inverse solution. The contents of this paper should be useful for the further application of the spherical parallel mechanism.

Kinematic solution of spherical Stephenson-III six-bar mechanism

A closed-form solution can be obtained for kinematic analysis of spatial mechanisms by using analytical method. However, extra solutions would occur when solving the constraint equations of mechanism kinematics unless the constraint equations are established with a proper method and the solving approach is appropriate. In order to obtain a kinematic solution of the spherical Stephenson-III six-bar mechanism, spherical analytical theory is employed to construct the constraint equations. Firstly, the mechanism is divided into a four-bar loop and a two-bar unit. On the basis of the decomposition, vectors of the mechanism nodes are derived according to spherical analytical theory and the principle of coordinate transformation. Secondly, the structural constraint equations are constructed by applying cosine formula of spherical triangles to the top platform of the mechanism. Thirdly, the constraint equations are solved by using Bezout’s elimination method for forward analysis and Sylvester’s resultant elimination method for inverse kinematics respectively. By the aid of computer symbolic systems, Mathematica and Maple, symbolic closed-form solution of forward and inverse displacement analysis of spherical Stephenson-III six-bar mechanism are obtained. Finally, numerical examples of forward and inverse analysis are presented to illustrate the proposed approach. The results indicate that the constraint equations established with the proposed method are much simpler than those reported by previous literature, and can be readily eliminated and solved.

Forward displacement analysis of a 3-RPR spherical parallel mechanism

The forward displacement analysis of spherical parallel mechanisms is a nonlinear problem and has attracted the attention of many researchers. A method is proposed to analyze the forward displacement of a 3-RPR spherical parallel mechanism. Firstly, based on spherical geometry and spherical trigonometry theory, a mathematical model is derived for the forward displacement analysis of the spherical parallel mechanism. After simplifying the mathematical model, the kinematical equations are then solved using the resultant elimination method. Using this method, one can obtain the three variables representing the position and pose of the moving platform directly. Finally, a numerical example is presented and Autodesk Inventor software is used to verify all the real solutions. The method of mathematical modeling, equation simplification, resultant elimination presented in this paper can be extended to solve similar problems effectively.

Analysis of Structural Parameter and Design of Elbow Joint Rehabilitation Parallel Robot

Elbow joint is one of the body's important joints, most of the activities of the human body are inseparable from the elbow joint, and including taking and holding movements.In order to increase the workspace of elbow joint, a novel elbow joint rehabilitation parallel robot based on 2-DOF orthogonal spherical parallel mechanism is proposed. First, the position inverse solution equation of elbow joint is established. Further, the workspace of elbow joint is analyzed. The optimal structural parameters are obtained by use of the objective function of optimization method. Finally, the virtual prototype of elbow joint rehabilitation parallel robot is designed using optimal structural dimensions parameters.

Kinematics Performance Analysis of a Robot Hip Joint

Kinematics research of mechanism is very important, the dynamic analysis and the design are based on linematics analysis. In this paper, a novel robot hip joint based on 3-RRR orthogonal spherical parallel mechanism is proposed, and Jacobin matrix is established. Then the linematics transmission performance evaluation index is defined. Furthermore the linematics transmission performance index is analyzed. The hip joint has good linematics transmission performance at the initial position. With the increase of workspace, linematics transmission performance gradually decreased. 3-RRR parallel mechanism is the ideal prototype of bionic robot and rehabilitation robot hip joint.

Parameter Optimization Design of a Novel Robot Shoulder Based on the Workspace

A robot shoulder joint should have good kinematic performance and workspace, but the structural parameters of shoulder joint directly affect the workspace. In order to increase the workspace of shoulder joint, a novel robot shoulder joint based on 3-DOF orthogonal spherical parallel mechanism is proposed. This paper studied the influence on its workspace affected by the variation of structural parameters of the connecting rod, frame connecting rod, rod diameter of this shoulder joint mechanism. Based on the consideration of mechanical constraint, the objective function of the optimal structural parameters of the shoulder joint is established. Having the maximum the workspace, the structural parameters of shoulder joint are gained.

Design Defects Immune Identification Methodology for Mechanical Products Based on Directed Graph of Assembly Constraint Relationship

In order to identify design defects in mechanical product quickly and accurately, geometric constraints relationships between mechanical parts are formulated as critical functions, assembly constraint relationship (ACR) matrix is established based on encoding of geometric constraints between mechanical parts. Directed graph is employed to describe constraint relationship of ACR matrix, the node in directed graph denotes parts number, data structure of node stores the design parameters of mechanical parts, weights of directed graph arcs represents geometric constraint type. Weights of directed graph arcs are treated as antigen, design defects for mechanical parts are treated as antibody, mutation rules such as trimming, splicing and replacement is employed to identify design defects of antigen gene. Identification example of spherical mechanism demonstrates effectiveness and accuracy of above methodologies.

Analysis of accelerations and nonlinear oscillations of a spherical mechanism of parallel structure

A spherical mechanism of parallel structure with three degrees of freedom is considered. A solution of the problem of acceleration and a study of the vibration of the mechanism are presented. Nonlinearity is defined by the geometry of allocation of the drives and their mutual influence.