Rotational Parallel Mechanism Research Articles

Analisis Perpindahan Mekanisme Paralel Tiga Derajat Kebebasan Rotasi Murni 3 -RRR

In this paper was studied displacement analysis of three degrees of freedom pure rotational parallel mechanism. The mechanism was constructed by three identical kinematic chains composed of three revolute joins named 3-RRR, moving platform and fixed body (base) where such as configuration was classified as over constraint mechanism. To develop the formulation of displacement analysis was employed six kinematic constants consisting of mounting angle of revolute joint on the platform and the base, position of mounting revolute joint on the platform and the base relative to the center of the platform and the base and distance between three revolute joint on the kinematic chains. It was obtained analytical formulation of the inverse displacement analysis of the 3-RRR pure rotational over constraint parallel mechanism which is clarified by the cad program.

Optimization of the Rotational Asymmetric Parallel Mechanism for Hip Rehabilitation With Force Transmission Factors

Abstract An asymmetric three-degree-of-freedom parallel mechanism is adopted in rehabilitation robots for assisting patients suffering from stroke or trauma in the hip. It is necessary to keep its kinematic singularity out of the workspace of human normal gait and increase the output power efficiency. Therefore, a novel method is proposed to optimize geometrical parameters of the mechanism. To describe the kinematic singularity in a better way, the improved force transmission indexes based on previous methods are proposed using the reciprocal product and mobility condition of the closed-loop mechanism. The indexes mainly represent the force transmission performance of unactuated parts of subchains and moving platform. Together with the driving force transmission indexes and geometrical constraints, the multiobjective optimization model is established. The differential evolution algorithm, which is widely applied to mechanism optimization, is used to achieve optimal results. The Jacobian matrix singularity and output power efficiency along giving trajectory before and after optimization are compared to verify the effectiveness of the method.

Type synthesis and kinematics analysis of a family of three translational and one rotational pick-and-place parallel mechanisms with high rotational capability

This article proposes a family of spatial three translational and one rotational parallel mechanisms (PMs) for pick-and-place operation. Their features are one independent rotation of the mechanism with four identical limbs, which are provided by the four revolute joints on the moving platform. The rotational capability of the PMs has a range of at least 180°. This article focuses on the synthesis of the PMs and kinematics analysis of the 4- P(2-SS)R parallel mechanism. First, based on the Lie group theory, three parallelograms are used in designing the PMs. The limbs are listed and two types of three translational and one rotational PMs are synthesized. Then, a typical 4- P(2-SS)R PM is selected, the 6 × 6 Jacobian matrix and the 6 × 6 × 6 Hessian matrix of the mechanism are derived for solving the displacement, velocity, and acceleration of the mechanism. Finally, singularity configurations are disclosed from the 6 × 6 Jacobian matrix, and the workspace of the mechanism is provided to illustrate the high rotational capability.

Spherical and Non-Spherical Combined Two Degree-of-Freedom Rotational Parallel Mechanism for a Microsurgical Robotic System

Microsurgery, often performed for anastomosis of small vessels and nerves, requires micro-manipulations of small tissues and thus requires highly specialized surgical skills. Robotic technology has great potential to assist with microsurgical treatments because of the high accuracy provided by robots; however, implementation remains challenging because the technical requirements of robotic surgery are far different from those in industry. One of the greatest challenges is that two surgical tools (e.g., tweezers) must be precisely and deftly moved around the surgical area in seven degrees of freedom (DOF) using one DOF to grasp each tool, and these tools are used in close proximity to each other. Additionally, high accuracy and rigidity at the tool tip are imperative for successful performance of the microsurgical procedure. In this study, we propose a new rotational two-DOF parallel mechanism that has the inherent advantages of a parallel mechanism, namely accuracy and rigidity, within a newly proposed spherical and non-spherical combined parallel structure to prevent collision of the two mechanisms in a dual-arm setup for microsurgery. The prototype was evaluated by performing a series of mechanical tests, and microsurgical suturing was performed by a microsurgical robotic system. The series of evaluations demonstrated the feasibility of the proposed mechanism.

Type synthesis of 1T2R parallel mechanisms with parasitic motions

Finite motion analysis and type synthesis of parallel mechanisms with parasitic motions are great challenges in the fields of mechanisms and robotics. This paper proposes a finite screw based approach to handle this problem by taking one translational and two rotational (1T2R) parallel mechanisms with parasitic motions as examples. Firstly, 1T2R finite motion of the moving platform is categorized into four cases whose finite motions are described by finite screw analytically and then the reasons for producing parasitic motions are explored in this process. Based on this, available limbs are obtained algebraically by deriving formulas formed by triangle screw product. Finally, the assembly conditions among limbs, fixed base and moving platform are acquired in an analytical manner, leading to synthesize 1T2R parallel mechanisms with parasitic motions systematically. This paper solves a long-term problem that describes and analyzes finite motions of parallel mechanisms with parasitic motions and synthesizes their topology structures.

A Soft Robotic Fish with Variable-stiffness Decoupled Mechanisms

A Body and/or Caudal Fin (BCF) fish modulate its body stiffness by mechanisms consisting of antagonistic muscles. The mechanisms can be considered as Redundant Planar Rotational Parallel Mechanisms (RPRPM) with antagonistic flexible elements. For a typical RPRPM, its stiffness consists of the adjustable stiffness resulting from internal forces and the inherent stiffness caused by inherent compliances of flexible elements. In order to decouple the adjustable stiffness from the inherent stiffness and expand the range of stiffness variation, a variable-stiffness decoupled mechanism based on the Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator (MACCEPA) is presented and used to construct a soft robotic fish with large stiffness variation. According to the analysis of the evolution from RPRPM to MACCEPA, it can be found that MACCEPA is just a special type of RPRPM with only an adjustable stiffness. In addition, MACCEPA existed before RPRPM mechanism. The prototype of the soft robotic fish with variable-stiffness decoupled mechanisms is built to explore the relationships between the body stiffness and the swimming performance. It is validated experimentally that the stiffness variation multiple of the robotic fish is raised, the swimming performance of the robotic fish is improved when the stiffness is modulated to match the driving frequency.

Producing negative active stiffness in redundantly actuated planar rotational parallel mechanisms

Generally, the Cartesian stiffness matrix of closed-loop mechanisms can be divided into the passive stiffness and the active stiffness. The passive stiffness was determined by the kinematic parameters and joint stiffness, while the active stiffness is sub-divided into the forced active stiffness KE, related to the external wrench, and active stiffness KIG generated by internal force. The passive stiffness is always positive definite, however, the active stiffness can be positive, semi-positive or negative definite. We exemplified it with a redundantly actuated planar rotational parallel mechanism (RAPR-PM), showing negative stiffness criteria for the active stiffness. Whether the elastic limbs are compressed or stretched, once the preload is known, the sign of the active stiffness can be determined from kinematic parameters. The results can be used to design variable stiffness mechanisms. Since some biological structures of animals, like fish, can be represented by a series of joint-linked RAPR-PMs, the conclusions in this paper can be extended to study the inherent stiffness mechanism of animals.

Variable-stiffness decoupling of redundant planar rotational parallel mechanisms with crossed legs

For redundant planar rotational parallel mechanisms (RPRPM), stiffness consists of active stiffness resulting from internal forces and passive stiffness caused by compliances of flexible elements, and the active stiffness is coupled with the passive stiffness. The stiffness variations with stretching internal force and compressing internal force of flexible elements are analyzed. By combining the leg-crossed RPRPM and leg-uncrossed RPRPM of different leg arrangements, the active stiffness is decoupled from the passive stiffness. The stiffness is modulated by changing the internal force and hence the spring stretching length independently to avoid being influenced by the passive stiffness. The stiffness variation multiple with given spring stretching length is maximized by decoupling the active stiffness from the passive stiffness. The variation of natural frequency of RPRPM is maximized by maximizing the stiffness variation, and the RPRPM can employ vibration of resonance to improve the working performance in a large range of driving frequency.

Type Synthesis of Uncoupled Rotational Parallel Mechanisms with Two Degrees of Freedom

Type Synthesis of Uncoupled Rotational Parallel Mechanisms with Two Degrees of Freedom

Type synthesis of 1T2R and 2R1T parallel mechanisms employing conformal geometric algebra

Abstracts This paper proposes an analytical method based on conformal geometrical algebra to implement and unify type synthesis of one translational and two rotational (1T2R) parallel mechanisms and two rotational and one translational (2R1T) parallel mechanisms. Firstly, conformal geometrical algebra is introduced in this paper to describe finite motions and carry out type synthesis of parallel mechanisms in an algebraic way. Secondly, the finite motions of 1T2R and 2R1T parallel mechanisms are described and their relations are explored, and this results in unifying the type synthesis of these two types of parallel mechanisms in the same procedure. Then, a parametric and algebraic generation method is proposed to obtain available limbs and axes layout of joints with these limbs. Finally, the assembly conditions among available limbs are given to synthesize systematically 2R1T parallel mechanisms with non-overconstrained or overconstrained property, as well as 1T2R parallel mechanisms with the same properties. This method proposed in this paper is valid in carrying out finite motion representation and type synthesis of parallel mechanisms in an algebraic and analytical way, and then is beneficial to an automatic manner using computer programming languages. Furthermore, the method may solve type synthesis of special parallel mechanisms, such as parallel mechanisms with varied output rotational axes.

Type synthesis and analysis of rotational parallel mechanisms with a virtual continuous axis

Having virtual continuous axes is an important mechanism performance required by the motion tracking and simulating mechanisms for large-scale heavy-weight apparatus. Mathematical criteria for a virtual continuous axis using virtual coefficient theory is proposed through geometric modeling continuous rotation of the constrained rigid body and a virtual continuous axis. A type of synthesis approach for rotational parallel mechanisms (RPMs) with a virtual continuous axis is given and a type of RPM with arc-rail-slider or cross slipper is constructed. On the basis of screw theory, degree of freedom (DoF) and properties of the axes of a typical RPM with a virtual continuous axis are analyzed, and the inputs selection and arrangement are also discussed. The kinematic and dynamic models of the RPM are established. Finally, a numerical example and a solution to the motion simulation for super-large-scale heavy-weight apparatus are given.

Type synthesis of 2-DoF rotational parallel mechanisms actuating the inter-satellite link antenna

This paper focuses on the type synthesis of two degree-of-freedom (2-DoF) rotational parallel mechanisms (RPMs) that would be applied as mechanisms actuating the inter-satellite link antenna. Based upon Lie group theory, two steps are necessary to synthesize 2-DoF RPMs except describing the continuous desired motions of the moving platform. They are respectively generation of required open-loop limbs between the fixed base and the moving platform and definition of assembly principles for these limbs. Firstly, all available displacement subgroups or submanifolds are obtained readily according to that the continuous motion of the moving platform is the intersection of those of all open-loop limbs. These subgroups or submanifolds are used to generate all the topology structures of limbs. By describing the characteristics of the displacement subgroups and submanifolds intuitively through employing simple geometrical symbols, their intersection and union operations can be carried out easily. Based on this, the assembly principles of two types are defined to synthesize all 2-DoF RPMs using obtained limbs. Finally, two novel categories of 2-DoF RPMs are provided by introducing a circular track and an articulated rotating platform, respectively. This work can lay the foundations for analysis and optimal design of 2-DoF RPMs that actuate the inter-satellite link antenna.

Type synthesis of two-degrees-of-freedom rotational parallel mechanism with two continuous rotational axes

The two-rotational-degrees-of-freedom(2R) parallel mechanism(PM) with two continuous rotational axes(CRAs) has a simple kinematic model. It is therefore easy to implement trajectory planning, parameter calibration, and motion control, which allows for a variety of application prospects. However, no systematic analysis on structural constraints of the 2R-PM with two CRAs has been performed, and there are only a few types of 2R-PM with two CRAs. Thus, a theory regarding the type synthesis of the 2R-PM with two CRAs is systematically established. First, combining the theories of reciprocal screw and space geometry, the spatial arrangement relationships of the constraint forces applied to the moving platform by the branches are explored, which give the 2R-PM two CRAs. The different distributions of the constraint forces in each branch are also studied. On the basis of the obtained structural constraints of branches, and considering the geometric relationships of constraint forces in each branch, the appropriate kinematic chains are constructed. Through the reasonable configuration of branch kinematic chains corresponding to every structural constraint, a series of new 2R-PMs with two CRAs are finally obtained.

Synthesis of branched chains with actuation redundancy for eliminating interior singularities of 3T1R parallel mechanisms

Although it is common to eliminate the singularity of parallel mechanism by adding the branched chain with actuation redundancy, there is no theory and method for the configuration synthesis of the branched chain with actuation redundancy in parallel mechanism. Branched chains with actuation redundancy are synthesized for eliminating interior singularity of 3-translational and 1- rotational(3T1R) parallel mechanisms. Guided by the discriminance method of hybrid screw group according to Grassmann line geometry, all the possibilities are listed for the occurrence of interior singularities in 3T1R parallel mechanism. Based on the linear relevance of screw system and the principles of eliminating parallel mechanism singularity with actuation redundancy, different types of branched chains with actuation redundancy are synthesized systematically to indicate the layout and the number of the branched chainsinterior with actuation redundancy. A general method is proposed for the configuration synthesis of the branched chains with actuation redundancy of the redundant parallel mechanism, and it builds a solid foundation for the subsequent performance optimization of the redundant actuation parallel mechanism.

Stiffness analysis of a 2-DoF over-constrained RPM with an articulated traveling platform

Driven by the requirements of inter-satellite link antenna for tracking mechanism with two degree-of-freedom (DoF), this paper proposes a 2-DoF over-constrained rotational parallel mechanism (RPM) with an articulated traveling platform and formulates its stiffness model considering gravitational effects. The stiffness modeling is implemented by three steps: 1) Considering the over-constrained property and gravitational effects, twist/wrench mapping models of two R(RU)2 limbs connecting the fixed base and the articulated traveling platform are obtained based upon screw theory. 2) Employing deformation superposition principle, the compliance models of two R(RU)2 limbs in their joint spaces are formulated, of which component compliance is described by n-DoF (n≤6) virtual springs; and 3) by applying deformation compatibility conditions and twist/wrench mapping models into the virtual work equations, the stiffness model of the 2-DoF over-constrained RPM considering gravitational effects is derived. From component, limbs to mechanism, the stiffness modeling process demonstrates their relations with clear physical meaning and unifies performances including kinematic, stiffness, accuracy and dynamics. This approach is verified by commercial FEA software. Finally the stiffness distribution and gravitational effects within prescribed workspace are discussed.

Elasto-dynamic analysis of a novel 2-DoF rotational parallel mechanism with an articulated travelling platform

This paper carries out the elasto-dynamic analysis of a novel 2 degrees-of-freedom (DoF) rotational parallel mechanism (RPM) with an articulated travelling platform by means of kineto-elasto dynamic method. The architecture of the proposed 2-DoF RPM is firstly described, and then its kinematic analysis is carried out by closed-loop vector method. On the basis of finite element analysis, the elasto-dynamic models of movable components are established before assembling to formulate the elasto-dynamic equations of the whole mechanism in the light of deformation compatibility conditions. The free vibration equation is then achieved to evaluate the natural frequency of the novel 2-DoF RPM. Finally, an example is illustrated and the results are verified by finite element software. It shows that the relatively high natural frequencies and good dynamic performance make the novel 2-DoF RPM a promising solution for pose-adjusting module of 5-DoF machine centre.

The Nonexistence of Three Degrees of Freedom Rotational Fully Decoupled Parallel Mechanism

The existence of coupling makes the parallel mechanism possess some special advantages over the serial mechanism, while it is just the coupling that brings about the parallel mechanism some difficulties in kinematics and dynamic analysis, the development of control system, and the trajectory planning. Therefore the research on the decoupled parallel mechanism becomes one of the hot of the mechanism fields. While whether the parallel mechanism can realize decouple is the premise for synthesis and analysis of the parallel mechanism. Based on screw theory, the existence of the three degrees of freedom (3-DoF) rotational fully-decoupled parallel mechanism is distinguished. Then taking the 6-PUS/UPU parallel mechanism as example, the rotation angles of the moving platform are measured, which is verified the impossibility of the 3-DoF rotation decoupling. The contents of this paper should possess theoretical significance for the innovative configuration synthesis and structure design of rotational decoupled parallel mechanism.

A Novel Two Degrees of Freedom Rotational Decoupled Parallel Mechanism

In the field of spatial orientation, the rotational parallel mechanism is widely used. While the existence of coupling brings about the parallel mechanism some difficulties in kinematics and dynamic analysis, the development of control system, and so on. This condition restricts the application fields and effects of the rotational parallel mechanism. Therefore, this paper proposes a novel 2-DOF (two degrees of freedom) rotational DPM (decoupled parallel mechanism). The feature of the mechanism is described and their movement form is analyzed with screw theory. The proposition of the novel rotational DPM will enrich the configurations of the parallel mechanism, and the contents of this paper should be useful for the further research and application of the rotational parallel mechanism.

Mobility and Singularity Analysis of a Class of Two Degrees of Freedom Rotational Parallel Mechanisms Using a Visual Graphic Approach

In this paper, a visual graphic approach is presented for the mobility and singularity analysis of mechanisms with no helical pair. The presented method is established upon the reciprocal screw system theory. Using the visual graphic approach, the mobility and singularity analysis mainly requires applying a few simple rules and involves into no formula derivation. As a case study, the mobility and singularity analysis is implemented for a class of two degrees of freedom (DOF) rotational parallel mechanisms (RPMs), including the Omni-Wrist III with four limbs and its two derived architectures with three limbs called the T-type and Δ-type RPMs. The Δ-type one is found to has kinematic properties close to the Omni-Wrist III.

Optimal design of a parallel mechanism with three rotational degrees of freedom

This paper presents the concept design of a pose-adjustment system applied in the large fuselage or wing assembly of aircraft manufacturing which including a 3-degree-of-freedom rotational parallel mechanism (3-DoFs RPM), pogo columns and three tracks. The optimal design of the 3-DoFs RPM with its topology a 3-PUS&S mechanism is detailed, which is designed as a rigid yet compact module that can act as a pose-adjustment mechanism moving along three long tracks for large aircraft structural component assembly, a middle fuselage for example. Inverse kinematics of the 3-DoFs RPM with the exponential product method is achieved to lay the foundation for its kinematic synthesis. Next, with the commercial mathematical software, one can get the reachable workspace and define the prescribed workspace, respectively. Then, dimensional synthesis of the 3-DoFs RPM is executed to achieve a relatively good kinematic performance within its workspace. With the commercial CAE software, stiffness analysis is carried out for performance evaluation of the 3-DoFs RPM virtual prototype.