Structural Condition for [PP]S Parallel Mechanism without Parasitic Motion

Parasitic motion is an important kinematic phenomenon in mechanisms and a generic property of lower mobility parallel mechanisms (PMs), such as: 3-RPS PM (R denotes a rotational joint, P a prismatic joint, and S a spherical joint), Z3 head machine tool (3-PRS PM), Exechon mechanism (2-UPR-SPR, U denotes a universal joint) and so on. Parasitic motions refer to some dependent motions that accompany with other independent motions. It may introduce some undesired motion components which lead to lower manipulation accuracy/quality and more difficulties in calibration. On the other hand, it may perform a motion task by using a lower degree of freedom (DOF) PM that leads to a lower cost, lower complexity of kinematics and easier controls. We should utilize the advantages of parasitic motions and reduce/shield the disadvantages. However, the research on the parasitic motion is far from being adequate. This paper investigates the essence of the parasitic motion and gives a simple identification method. Firstly, the definitions and order of parasitic motions are discussed. Secondly, three classifications of parasitic motions are presented according to the property, amplitude and motion pattern. Then, an equation and corresponding method are detailed to identify the parasitic motion. Some examples are given to illustrate the method. Finally, the means are proposed to reduce/shield or utilize parasitic motion.

We perform extensive molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles in two dimensions that interact via purely repulsive contact forces. We measure the structural relaxation times obtained from the long-time α decay of the self part of the intermediate scattering function for the translational and rotational degrees of freedom (DOF) as a function of packing fraction φ, temperature T, and aspect ratio α. We are able to collapse the packing-fraction and temperature-dependent structural relaxation times for disks, and dimers and ellipses over a wide range of α, onto a universal scaling function F(±)(|φ-φ(0)|,T,α), which is similar to that employed in previous studies of dense liquids composed of purely repulsive spherical particles in three dimensions. F(±) for both the translational and rotational DOF are characterized by the α-dependent scaling exponents μ and δ and packing fraction φ(0)(α) that signals the crossover in the scaling form F(±) from hard-particle dynamics to super-Arrhenius behavior for each aspect ratio. We find that the fragility of structural relaxation at φ(0), m(φ(0)), decreases monotonically with increasing aspect ratio for both ellipses and dimers. For α>α(p), where α(p) is the location of the peak in the packing fraction φ(J) at jamming onset, the rotational DOF are strongly coupled to the translational DOF, and the dynamic scaling exponents and φ(0) are similar for the rotational and translational DOF. For 1<α<α(p), the translational DOF become frozen at higher temperatures than the rotational DOF, and φ(0) for the rotational degrees of freedom increases above φ(J). Moreover, the results for the slow dynamics of dense liquids composed of dimer- and ellipse-shaped particles are qualitatively the same, despite the fact that zero-temperature static packings of dimers are isostatic, while static packings of ellipses are hypostatic. Thus, zero-temperature contact counting arguments do not apply to structural relaxation of dense liquids of anisotropic particles near the glass transition.

Background: The parallel mechanism plays an important role in various fields. The multifunctional integrated innovation experiment platform can improve the utilization rate of the mechanism and be applied in many fields. Objective: The main objective of the study is to establish an integrated innovation experiment platform based on the 3-PRS parallel mechanism, which can be used in typical application and related technology development. Methods: The integrated innovation experiment platform is established and analyzed based on the 3-PRS parallel mechanism. According to the 3D model of the experiment platform, the kinematics and dynamics are analyzed. The force/position control strategy of the system is adopted. According to the function of the experiment platform, two kinds of application and the position and pose measurement technology are developed. The experiment platform is developed by the following methods: (1) The XY table is set up on the fixing platform of the 3-PRS parallel mechanism, so that the mechanism has five degrees of freedom, and the many kinds of workpiece can be easily processed. (2) By selecting the impedance parameter, the experiment platform can realize the compliant control of plantar flexion/dorsiflexion and varus/eversion simultaneously. (3) The binocular vision position and pose measurement method is used to obtain the marked images of the experiment platform through dual cameras, and the position and pose is obtained through image processing, 3D reconstruction and stereo matching, etc. (4) The position and pose detection based on deep learning is divided into two parts: one is to detect the slider height using the regression Convolutional Neural Network (CNN); the other is to compute the position and pose using the Back Propagation Neural Network (BPNN). Results: The experiment results show that the function of the 3-PRS parallel mechanism integrated innovation experiment platform can be effectively realized. The position and pose can be accurately measured in real time using the proposed two measurement methods. The impedance parameters are selected to achieve the rehabilitation training function of the 3-PRS ankle rehabilitation robot and the characters are processed to verify the function of the 3-PRS-XY series-parallel machine tool. Conclusion: The integrated innovation experiment platform based on the 3-PRS parallel mechanism can achieve the function of mechanical processing and rehabilitation training, and can also measure the state of motion in real time through machine vision and deep learning.

Aiming at the problem that the existing 2R1T (two rotations and one translation) vehicle engine motion simulation platform mechanism cannot realistically simulate the motion state of the engine due to the parasitic motion. In this paper, the geometric relationship between the restraint force of the branch and the rotation axis of the 2R1T parallel mechanism(PM) is analyzed. A construction criterion of the branch for redundant mechanism without parasitic motion is proposed. From the perspective of mechanism innovation design, a novel 2-RPS/2-UPS/PS PM with large bearing capacity without parasitic motion is designed. This paper solves the problem that the existing 2R1T PM without parasitic motion cannot be applied to the occasion of large load. The kinematics analysis of the mechanism is carried out, and the characteristic of the mechanism without parasitic motion is verified. The workspace of the mechanism is calculated. And the kinematics simulation analysis, stress analysis and prototype experiment of the mechanism are carried out. The correctness of the design index of the motion simulation platform and the characteristic of the mechanism without parasitic motion is proved. It provides a theoretical basis for the application of the mechanism without parasitic motion in large load-bearing occasions.

In this paper, a novel 3-UPU (P and U stand for prismatic and universal joints, respectively) parallel mechanism (PM) and its variant PM are proposed. Both of them have two rotational and one translational (2R1T) degrees of freedom (DOFs) without involving any parasitic motion. Mobility analysis shows that the three constraint forces provided by three limbs of the mechanism are located on the same plane and the mobile platform can translate perpendicular to this plane and rotate around any axis on it. Analysis of the mechanism’s motion characteristics demonstrates that the mobile platform outputs either pure rotation or pure translation. Moreover, the rotational axis can be fixed during the rotation process, which means no parasitic motion is involved. The causes of the motion characteristics are analyzed by the combination of an overall Jacobian matrix, a statistical method, and a geometric method. The PMs only need to translate or rotate once to move from the initial configuration to the final configuration, which allows for easy control of speeds. The relationship between mechanism parameters and singularity is analyzed. A speed control method for the PMs is proposed and a prototype is designed and made. Experiments are conducted to verify the determined motion characteristics, the speed control method, and the singularity analysis.

Folded beam waveguide absorbers (WGAs) have been shown to be effective low-frequency damping devices. Early WGA studies were unable to accurately predict this damping behavior. These studies used only translational degrees of freedom (DOFs), which resulted in the underestimation of the WGA damping performance. A recent study [Munro and Hambric, ‘‘Modeling folded beam waveguide absorber behavior using translational and rotational degree of freedom frequency response function coupling,’’ Proc. NOISE-CON 2003] used translational and rotational DOF frequency response functions to predict folded beam WGA behavior when attached to a thick rectangular plate, where the plate and WGA rotational DOFs were estimated using the finite-differencing method. Each plate and WGA DOF was coupled independently using frequency domain substructure synthesis (FDSS) [Jetmundsen et al., ‘‘Generalized frequency domain synthesis,’’ J. Am. Helicopter Soc. 55–64, Jan (1988)], and the damping contributions due to each DOF were summed to give the total WGA damping prediction. This method gives a much improved damping estimate from previous methods but is inefficient for complex problems. In this study, all the DOFs for the plate and WGA are combined simultaneously using FDSS to predict the WGA damping behavior and plate response with folded beam WGAs attached.

This paper presents an approach of utilizing parasitic motion compensation for designing high-precision flexure mechanism. This approach is expected to improve the accuracy of flexure mechanism without changing its degree of freedom (DOF) characteristic. Different from the method which mainly concentrates on how to compensate the parasitic translation error of a parallelogram-type flexure mechanism existing in most of the literatures, the proposed approach can compensate the parasitic motion produced by rotation in company with translation. Besides, the parasitic motion of a flexure mechanism is formulated and evaluated by utilizing its compliance. To specify it, the compliance of a general flexure mechanism is calculated firstly. Then the parasitic motions introduced by both rotation and translation are analyzed by utilizing the resultant compliance. Subsequently, a compliance-based compensation approach is addressed as the most important part of this paper. The design principles and procedure are further proposed in detail to help with improving the accuracy of the flexure mechanism. Finally, a case study of a 2R1T flexure mechanism is provided to illustrate this approach, and FEA simulation is implemented to demonstrate its validity. The result shows that it is a robust design method for the design of high-precision flexure mechanism.

This paper concerns the proposal and analysis of a novel spatial parallel manipulator. The parallel manipulator consists of a base plate, a movable platform, and three connecting legs. The moving platform has three degrees of freedom (DoFs), which are two degrees of translational freedom and one degree of rotational freedom, with respect to the base plate. The inverse and forward kinematics problems are described in closed forms and the velocity equation of the new parallel manipulator is given. Three kinds of singularities are presented. The workspace for the manipulator is analyzed systematically. Especially, the indices to evaluate the rotational capability of the moving platform of the manipulator will be defined and discussed in detail. Due to the high rotational capability performance, the proposed manipulator has wide application in the fields of industrial robots, simulators, micromotion manipulators, and parallel kinematic machines.

Analysis of a novel cylindrical 3-DoF parallel robot

The results of 2-D numerical simulations of non-equilibrium hypersonic flow of a diatomic gas, e.g., nitrogen past a 2-D blunt body at low to high Knudsen Numbers are presented. The flow field is computed using the Generalized Boltzmann (or the Wang-Chang Uhlenbeck [1]) Equation (GBE) for Kn varying from 0.1 to 10. In the GBE [2], the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively. The computational framework available for the classical Boltzmann equation (for a monoatomic gas with translational degrees of freedom) [3] is extended by including the rotational degrees of freedom in the GBE. The general computational methodology for the solution of the GBE for a diatomic gas is similar to that for the classical BE except that the evaluation of the collision integral becomes significantly more complex due to the quantization of rotational energy levels. The solution of GBE requires modeling of transition probabilities, elastic and inelastic cross-sections etc. of a diatomic gas molecule, needed for the solution of the collision integral. An efficient computational methodology has been developed for the solution of GBE for computing the flow field in diatomic gases at high Mach numbers. There are two main difficulties encountered in computation of high Mach number flows of diatomic gases with rotational degrees of freedom using the GBE: (1) a large velocity domain is needed for accurate numerical description of molecular velocity distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 to 70 energy levels are needed for accurate representation of the rotational spectrum of the gas. These two problems result in very large CPU and memory requirements for shock wave computations at high Mach numbers (> 6). Our computational methodology has addressed these problems, and as a result efficiency of calculations has increased by several orders of magnitude. The code has been parallelized on a SGI Origin 2000, 64 R12000 MIPS processor supercomputer.

This is the first of a two part paper on three‐dimensional finite elements with rotational degrees of freedom (DOF). Part I introduces an 8‐node solid hexahedron element having three translational and three rotational DOF per node. The corner rotations are introduced by transformation of the midside translational DOF of a 20‐node hexahedron element. The new element produces a much smaller effective band width of the global system equations than does the 20‐node hexahedron element having midside nodes.A small penalty stiffness is introduced to augment the usual element stiffness so that no spurious zero energy modes are present. The new element passes the patch test and demonstrates greatly improved performance over elements of identical shape but having only translational DOF at the corner nodes.

A novel parallel mechanism with bifurcated motion is introduced by integrating a discontinuously movable mechanism in the limb design. The mechanism has instantaneously six degrees of freedom at a singularity point. With the discontinuously movable mechanism moving to different motion branches, the parallel mechanism has the ability to evolve into four configurations with different motion characteristics, including 3T motion configuration, 3R motion configuration, 2T1R motion configuration and 2R1T motion configuration. By rigidizing the input joints, the rationality of input scheme for this mechanism is identified based on screw theory. Six motors nearly mounted to the base can sufficiently drive the parallel mechanism to switch between different motion configurations and perform different motions. The forward and inverse kinematics of the mechanism in different configurations are given. The translational motions are independent with each other and decoupled with the rotational motions. Kinematics simulation is performed for the parallel mechanism and the results show that theoretical analyses are correct. The workspace of the parallel mechanism in a general configuration is given. Key words}Discontinuously movable mechanism Parallel mechanism Bifurcated motion Kinematics

Friction stir welding (FSW) has recently emerged as a solid-joining technology for high-strength aluminum alloys and light metal welding. The large axial force to be maintained between the welding tool and workpiece is the primary requirement of FSW process, which has also been a great obstacle to the design and application of FSW in manufacturing. Further complicating the issue is the need to perform FSW over three-dimensional contours, which requires a mechanism dexterous enough to set the stir pin used in welding to track a predefined trajectory with prescribed poses. Apart from the position specification, the design of a dexterous mechanism to pose the orientation of stir pin is a great challenge. This paper proposed the application of 3-PRS (P, R, and S standing for prismatic, revolute, and spherical joint, respectively) parallel mechanism as a welding tool head and employed it to form a five-axis welding machine tool for FSW. In order to accommodate the orientation capability requirements, the kinematic feature has been analyzed. With the dimensionless treatment of the Jacobian matrix of 3-PRS manipulator, a global condition index is proposed to estimate the kinematic dexterity in the whole orientation workspace. Finally, by means of an optimal design method and performance atlas, optimal designs of the 3-PRS parallel mechanism is carried out. A preferable set of optimized geometric parameters are obtained to achieve a compact and dexterous design, and the optimization results are used in development of a prototype machine for FSW.

A novel type synthesis method for a class of spatial multi-loop coupled mechanisms with translational degrees of freedom is proposed in the paper. The novel class of spatial multi-loop coupled mechanisms has a stable topology layout which consists of three branches and three coupled chains. The basic idea of the new structural synthesis method lies at replacing the inputs of one mechanism by the outputs of another, thereby combining several mechanisms, where the topology split method for the topological layout and corresponding degree of freedom splitting principle are provided. The synthesis of the target mechanism is transformed into synthesis of corresponding serial and parallel mechanisms thereby, and a class of spatial multi-loop coupled mechanisms is synthesized. To validate the new synthesis method and to present a theoretical basis for future application, kinematic analysis of a single translational mobility (1T) spatial multi-loop coupled mechanism and a symmetrical two translational degrees of freedom (2T) spatial multi-loop coupled mechanism is performed. This article enriches the family of the spatial mechanisms for further instructing the study of spatial multi-loop coupled mechanisms.

Parasitic motion is undesired in precision mechanisms, it causes unwanted kinematics. These erroneous motions are especially apparent in compliant mechanisms. Usually an analysis of parasitic motion is only valid for one type of mechanism. Kinematic information is imbedded in the compliance matrix of any mechanism; an eigenscrew decomposition expresses this kinematic information as screws. It uses screw theory to identify the lines along which a force yields a parallel translation and a rotation yields a parallel moment. These lines are called eigenwrenches and eigentwists. Any other load on the compliant mechanism will lead to parasitic motion. This article introduces two parasitic motion metrics using eigenscrew decomposition: the parasitic resultant from an applied screw and the deviation of an actual degree of freedom from a desired degree of freedom. These metrics are applicable to all compliant mechanism and allow comparison between two compliant mechanisms. These metrics are applied to some common compliant mechanisms as an example.