3-RPS Parallel Mechanism Research Articles

Research on novel hybrid structure AACMM based on 3-RPS parallel mechanism

Abstract The articulated arm coordinate measuring machine (AACMM), widely utilized in the field of industrial measurement, is assessed based on key performance indicators such as measurement accuracy, measurement space, and flexibility. To enhance these aspects of the AACMM, this paper introduces a novel type of AACMM. The new model is based on a 3-RPS (revolute joint R, prismatic joint P, spherical joint S) parallel mechanism (3-RPSPM). The working principle of the 3-RPSPM is detailed, and a corresponding computational model is established. An algorithm is proposed based on this mathematical model to determine the theoretical achievable accuracy of the 3-RPSPM. Additionally, a spatial error analysis of the 3-RPSPM is conducted to verify its compliance with AACMM accuracy requirements and to demonstrate a certain level of accuracy improvement. Through simulation analysis, the differences in measurement accuracy, measurement space, and flexibility between the new type of AACMM based on the 3-RPS parallel mechanism (3-RPSAACMM) and traditional AACMMs are compared. The results indicate that the 3-RPSAACMM, with its novel parallel structure free from series accumulation errors, not only maintains measurement flexibility but also achieves improvements in measurement accuracy and space. The hybrid structure adopted by the new 3-RPSAACMM offers a new direction for the future development of AACMMs, presenting significant research value and application prospects.

Multi-dimensional vibration isolating properties of a 3-RPS parallel damping seat

This paper proposes a new control scheme that is composed by the sliding mode control(SMC) with three-dimensional ceiling control to reduce the multi-dimensional vibration of the vehicle’s seat. The seat suspension system is made of a kind of 3-RPS parallel mechanism, in which each limb is mainly composed by the spherical pair, spring, piston rod, damping fluid and rotary pair. Based on the single-open-chain theory, Position and Orientation Characteristics (POC) set of a 3-RPS seat mechanism was analyzed to verify its movement law. Three-dimensional seat system mathematical model was established, and the SMC and ceiling control were combined to obtain the required force. The ceiling control belongs to an ideal control method, it could provide the reference for the SMC. The comparisons between the SMC and passive seat suspension system were done when the vehicles were walking or working on E, F and G-roads. The results show that the transient amplitudes of seat acceleration outputs were reduced with the proposed control scheme. The research in this work can be extended and applied for other vehicles and improve their performance.

Topological relation expression and verification of symmetrical parallel mechanism based on the evolution of chemical molecule

AbstractThe research of parallel mechanism (PM) configuration involves many problems. From topology to configuration, dimensional constraint, etc., how to establish the relationship between topology and configuration with effective methods is a long-term challenge for the configuration design. In this paper, the chemical molecular spatial structure (CMSS) is linked with the configuration of symmetrical parallel mechanism (SPM). Starting from the methane molecule (CH4), a spatial structural topological relation is obtained. Based on graph theory and the spatial structural topological relation, a new expression method with topological graph and its kinematic pair adjacency matrix for spatial SPM is proposed. Then, the expression and analysis for the characteristics of spatial SPM are obtained. Finally, by taking the 3-RPS PM and the 3-RRC PM as examples, the effectiveness and corresponding consistency of the proposed expression method are successfully verified. The proposed new expression method paves the way for the subsequent digital and automated design and analysis of the SPM configuration.

Kinematic Analysis and Workspace Investigation of Novel 3-RPS/(H) Metamorphic Parallel Mechanism

Abstract 3-RPS/(H) Metamorphic parallel mechanism based on conventional mechanisms is proposed in this study. In contrast to the 3-RPS mechanism, the 3-RPS/(H) mechanism comprises a novel intermediate metamorphic limb. The different constraints provided by the intermediate metamorphic limb and locking device enhance the dexterity of the metamorphic parallel mechanism. The configurations of the 3-RPS/(H) metamorphic parallel mechanism are analyzed and their degrees-of-freedom are obtained. Additionally, an inverse kinematic analysis of the mechanism is performed, and its workspace is compared with that of a conventional 3-RPS parallel mechanism with similar parameters. The results demonstrate that the 3-RPS/(H) metamorphic parallel mechanism exhibits better dexterity than that of the 3-RPS mechanism. Moreover, the effects of different structural parameters of the metamorphic parallel mechanism on the workspace are analyzed. Finally, the singularity analysis of the mechanism is performed. The results provide a theoretical basis for the design and optimization of mechanical legs.

Kinematic Comparisons of Hybrid Mechanisms for Bone Surgery: 3-PRP-3-RPS and 3-RPS-3-PRP

This paper proposes an approach to derive the Jacobian matrix of a hybrid mechanism by applying a velocity operator to the transformation matrix. This Jacobian matrix is capable of deducing hybrid singularities, which cannot be identified by using the screw-based Jacobian or velocity-based Jacobian. The transformation matrix was obtained based on the algebraic geometry approach, and it becomes the key point since it was used to not only formulate the Jacobian matrix, but also to define the motion type of hybrid mechanisms. In this paper, two hybrid mechanisms were investigated, which were composed of two distinct parallel mechanisms mounted in series. Hybrid Mechanisms 1 and 2 were composed of 3-PRP-3-RPS and 3-RPS-3-PRP (the underlined P is an actuated joint), respectively. The motion types of Hybrid Mechanisms 1 and 2 were determined from the product of the transformation matrices of the 3-PRP and 3-RPS parallel mechanisms, and vice versa. The developed method was employed to establish the Jacobian matrix to which the conditioning index was applied. Therefore, the kinematic performances of the two hybrid mechanisms can be compared for a given bone surgery trajectory within the workspace. It turns out that Hybrid Mechanism 1 has superior performance than that of Mechanism 2, which indicates that Mechanism 1 is better at transmitting power to the moving platform.

Kinematic Performance and Static Analysis of a Two-Degree-of-Freedom 3-RPS/US Parallel Manipulator With Two Passive Limbs

Abstract In this paper, a new 3-RPS (the limb consisting of one revolute, one prismatic, and one spherical joint)/US (universal joint and spherical joint) parallel mechanism with two degrees-of-freedom (DOFs) is obtained by adding a US passive limb into the 3-RPS parallel mechanism with the aim of obtaining a high load-bearing capacity. The moving platform possesses two rotational motions, analyzed by the Grassmann line geometry and screw theory. Then, the kinematic performance of the mechanism is analyzed, including inverse kinematics, overall Jacobian matrix, workspace, and singularity. On this basis, the mapping between the driving force and the load on the moving platform is deduced and verified by simulation. Next, the static of the proposed parallel mechanism is compared with that of the 3-RPS mechanism. The results show that the load-bearing capacity of the mechanism is improved by introducing the US passive limb. Finally, a case study verifies the potential application of the mechanism as a dual-axis tracking photovoltaic bracket.

Analysis of dynamic modeling and solution of 3-RPS parallel mechanism based on conformal geometric algebra

Analysis of dynamic modeling and solution of 3-RPS parallel mechanism based on conformal geometric algebra

Design and Dynamic Modeling of a 3-RPS Compliant Parallel Robot Driven by Voice Coil Actuators.

In order to increase the driving force of the voice coil actuator while reducing its size and mass, the structural parameters of the coil and magnet in the actuator are optimized by combing Biot–Savart law with Lagrangian interpolation. A 30 mm × 30 mm × 42 mm robot based on a 3-RPS parallel mechanism driven by voice coil actuators is designed. The Lagrangian dynamic equation of the robot is established, and the mapping relationship between the driving force and the end pose is explored. The results of dynamic analysis are simulated and verified by the ADAMS software. The mapping relationship between the input current and the end pose is concluded by taking the driving force as the intermediate variable. The robot can bear a load of 10 g. The maximum axial displacement of the robot can reach 9 mm, and the maximum pitch angle and return angle can reach 40 and 35 degrees, respectively. The robot can accomplish forward movement through vibration, and the maximum average velocity can reach 4.1 mm/s.

Instantaneous mobility analysis using the twist space intersection approach for parallel mechanisms

This paper focuses on instantaneous mobility analysis of parallel mechanisms using the twist space intersection approach. In this study, a nullspace-associated approach is first presented to determining the intersection of screw systems based on screw theory and linear algebra. The approach provides a way of investigating the motion-screw system of the platform for parallel mechanisms without constraint analysis. By investigating the order of the motion-screw system of a platform, this paper presents the instantaneous mobility of a 3-revolute-prismatic-spherical (3-RPS) parallel mechanism, that of a Bennett mechanism, that of a revolute-cylindrical-prismatic-prismatic (RCPP) mechanism and that of a 3-prismatic-universal-prismatic (3-PUP) parallel mechanism. This way of examining the mobility is equivalent to the way based on constraint analysis, presenting the validity of the presented approach and the correctness of instantaneous mobility analysis using the twist space intersection approach for parallel mechanisms and for overconstrained mechanisms.

Chasles' Motion Sphere—A Useful Tool to Visually Express the Motion Characteristics Over the Workspace of Robotic Mechanisms

Abstract This paper presents a useful concept/tool, i.e., Chasles' motion sphere (CMSphere), that is able to visually express the motion characteristics over the workspace and capable of investigating the local motion performance of the end-effector of robotic mechanisms. The process of CMSphere generation is in line with people's habit of observing a mechanism. Under a researched pose, give a small pose change to the end-effector by translating with a small length or rotating with a small angle along a direction, then the corresponding Chasles' motion of the small pose change can be calculated. Two key parameters of Chasles' motion, the pitch and the position of the Chasles' axis, are chosen to represent the motion characteristics. This kind of mathematical operation can be carried along many directions to obtain a distribution of the motion characteristics at the researched pose, which can be drawn as a sphere. To illustrate this tool, Robotic Mechanisms with Three Independent Pose Variables (RMTIPVs) are discussed as the research objects. Three categories of RMTIPVs based on the types of independent pose variables are given. For each category, the detailed process of CMSphere generation is discussed. The 3R series mechanism, Tricept, and 3-RPS (the limb consisting of one revolute, one prismatic and one spherical joints) parallel mechanism are used as examples to demonstrate the methodology.

Analysis of a three-extensible-rod tracker based on 3-RPS parallel manipulator for space large deployable paraboloid structure with power and communication integration

The combination of a solar array and a communication antenna can reduce the entire mass, physical size, and cost in space applications. Currently, related studies mainly focus on the combination of the two structures on one flat plate structure (FPS). Compared with the FPS, a paraboloid structure has lower surface density and higher conversion efficiency. Therefore, the novel design of a space large deployable paraboloid structure with power and communication integration (SSPCI) is proposed for spacecraft on a sun synchronous earth orbit. A novel three-extensible-rod (TER) tracker is studied in detail for the SSPCI to track the sun for power in the sunshine region or turn to face the ground station for communication in the earth's shadow region. The proposed TER tracker includes three extensible rods, where one end of each rod is connected to the base platform by a rotary joint, and the other end is connected to the mobile platform by a smart compound joint as a substitute for a spherical joint; this is known in the literature as a 3-RPS parallel mechanism. In contrast to existing serial mechanisms, it provides a simple and lightweight structure, high structural stiffness, low inertia, and more accurate positioning and pointing of the mobile platform. Meanwhile, the linear extensible rods used in the TER tracker help to reduce energy consumption, and do not require the use of large and heavy speed reducers. A kinematic model of the TER tracker is also established. Based on this kinematic model, a dynamic model is then derived by using Newton–Euler formulation. The motion trajectory of the TER tracker is planned for the SSPCI to track the sun or turn to face the ground station. By setting related parameters, the workspace and pointing accuracy of the TER tracker are analyzed and found to be satisfactory for the SSPCI, and the motion process of tracking the sun or turning to face the ground station is simulated to test the theoretical analysis. The driving force and consumed energy of the TER tracker are obtained; the results shows that the TER tracker is able to drive the SSPCI to track the sun or turn to face the ground station with the aforementioned advantages and small energy consumption. By using finite element analysis, the SSPCI supported by the TER tracker is found to have satisfactory structural performance at different orientations in a zero gravity state. Meanwhile, the TER tracker has a satisfactory operation life and can adapt well to the space thermal environment. Finally, preliminary sun tracking experiments on the TER tracker are performed on the ground successfully, indirectly proving its feasibility of the TER tracker from the mechanism principle and control mode in space applications.

Comparative Study on Two Solutions of 3-RPS Parallel Mechanism Pose

In this paper, the performance of the different methods for solving the pose of parallel mechanism is different in the amount and precision of calculation. Taking typical 3-RPS parallel mechanism as the analysis object, kinematics models of the mechanism were established with quaternion and Rodriguez parameter method respectively, and the bar length of the maximum reachable space was solved by genetic algorithm, so as to compare the advantages and disadvantages of the solution of the model. Finally, numerical simulation is used to compare the amplitude and fluctuation degree of the curve according to the smooth spline interpolation in both calculation and precision. The results show that the Rodriguez parameter method is superior to the quaternion method in the accuracy of pose resolution of 3-RPS parallel mechanism, while the quaternion method is superior in the real-time performance of the solution. This result provides a theoretical basis for the pose control of parallel mechanism.

A novel serial–parallel hybrid worm-like robot with multi-mode undulatory locomotion

Inspired by the morphology characteristics of segmented worms and the combination properties of serial–parallel structures, a novel serial–parallel hybrid worm-like robot with nine degrees of freedom (DOFs) is proposed. This robot is constructed of two symmetrically arranged 3-RPS parallel mechanisms (PMs) with single-DOF expandable platforms. According to the retrograde peristaltic wave that the locomotion mechanism of segmented worms and the kinematics of the robot, four basic gaits of three undulation modes are developed, including start-up adjustment gait and straight-going gait of rectilinear mode, turning gait of lateral undulation mode, and stair-climbing gait of vertical undulation mode. Based on which, the locomotion performance of the robot on four typical terrains including the stair, the slope, the gap, and the narrow passage is discussed. Then the corresponding locomotion controller is designed. Finally, a prototype is manufactured, the experiment results show that the robot can move in an arbitrary given direction for any given distance, and the practical locomotion performance coincides to the theoretical analysis.

Fast forward kinematics algorithm for real-time and high-precision control of the 3-RPS parallel mechanism

A new forward kinematics algorithm for the mechanism of 3-RPS (R: Revolute; P: Prismatic; S: Spherical) parallel manipulators is proposed in this study. This algorithm is primarily based on the special geometric conditions of the 3-RPS parallel mechanism, and it eliminates the errors produced by parasitic motions to improve and ensure accuracy. Specifically, the errors can be less than 10–6. In this method, only the group of solutions that is consistent with the actual situation of the platform is obtained rapidly. This algorithm substantially improves calculation efficiency because the selected initial values are reasonable, and all the formulas in the calculation are analytical. This novel forward kinematics algorithm is well suited for real-time and high-precision control of the 3-RPS parallel mechanism.

Micro machine tool oriented optimum design of 3-RPS parallel mechanism with large titling and uniform deflecting capacities

Micro machine tool oriented optimum design of 3-RPS parallel mechanism with large titling and uniform deflecting capacities

Position and orientation characteristics of robot mechanisms based on geometric algebra

The operable representation of robot mechanisms is the key to the computerization of type synthesis of parallel mechanisms (PMs). Geometric algebra, an effective mathematical tool for geometric representation and computation, is introduced to describe the position and orientation characteristics (POC) of robot mechanisms, including serial and parallel mechanisms, in this paper. According to the correspondence between the POC of the joint axis and the motion output characteristics of the moving link, the POC union is defined by the outer product operation for the serial kinematic chain and the POC intersection is defined by the shuffle product operation for the parallel kinematic chain. In this paper, a moving coordinate system independent of the position of a mechanism is established for the expression of the joint axes. The direct symbolic algorithm for the motion output characteristics of robot mechanisms, including union and intersection, is proposed and validated via several case studies of 3R open chain, Sarrus linkage, 3-RCC PM and 3-RPS PM. The analysis procedure shows intuition and explicitness that is suitable for computer-aided derivation of the POC set of a mechanism.

Mobility Analysis of Limited-Degrees-of-Freedom Parallel Mechanisms in the Framework of Geometric Algebra

Mobility is a basic property of a mechanism. The aim of mobility analysis is to determine the number of degrees-of-freedom (DOF) and the motion pattern of a mechanism. The existing methods for mobility analysis have some drawbacks when being applied to limited-DOF parallel mechanisms (PMs). Particularly, it is difficult to obtain a symbolic or closed-form expression of mobility and its geometric interpretations are not always straightforward. This paper presents a general method for mobility analysis of limited-DOF PMs in the framework of geometric algebra. The motion space and constraint space of each limb are expressed using geometric algebra. Then the mobility of the PM can be calculated based on the orthogonal complement relationship between the motion space and the constraint space. The detailed mobility analyses of a 3-RPS PM and a 3-RPC PM are presented. It is shown that this method can obtain a symbolic expression of mobility with straightforward geometric interpretations and is applicable to limited-DOF PMs with or without redundant constraints. Without solving complicated symbolic linear equations, this method also has computational advantages.

Compliance analysis of a 3-DOF spindle head by considering gravitational effects

The compliance modeling is one of the most significant issues in the stage of preliminary design for parallel kinematic machine(PKM). The gravity ignored in traditional compliance analysis has a significant effect on pose accuracy of tool center point(TCP) when a PKM is horizontally placed. By taking gravity into account, this paper presents a semi-analytical approach for compliance analysis of a 3-DOF spindle head named the A3 head. The architecture behind the A3 head is a 3-RPS parallel mechanism having one translational and two rotational movement capabilities, which can be employed to form the main body of a 5-DOF hybrid kinematic machine especially designed for high-speed machining of large aircraft components. The force analysis is carried out by considering both the externally applied wrench imposed upon the platform as well as gravity of all moving components. Then, the deflection analysis is investigated to establish the relationship between the deflection twist and compliances of all joints and links using semi-analytical method. The merits of this approach lie in that platform deflection twist throughout the entire task workspace can be evaluated in a very efficient manner. The effectiveness of the proposed approach is verified by the FEA and experiment at different configurations and the results show that the discrepancy of the compliances is less than 0.04 μm/N−1 and that of the deformations is less than 10μm. The computational and experimental results show that the deflection twist induced by gravity forces of the moving components has significant bearings on pose accuracy of the platform, providing an informative guidance for the improvement of the current design. The proposed approach can be easily applied to the compliance analysis of PKM by considering gravitational effects and to evaluate the deformation caused by gravity throughout the entire workspace.

Kinematical Simulation of 3-DOF Parallel Mechanism Based on ADAMS

Kinematics analysis of mechanism refers to analysis for pose、speed and acceleration of mobile platform of spatial 3-RPS parallel mechanism. In this paper, mathematical model of spatial 3-RPS parallel mechanism is primarily built, and the close loop equation is adopted for the positional posture analysis of the mobile platform, then the positional posture of mobile paltform is acquired. Finally, kinematical simulation will be acquired by software Adams, which makes sense in kinematical performance of spatial 3-RPS parallel mechanism.

Compliance modeling and analysis of a 3-RPS parallel kinematic machine module

The compliance modeling and rigidity performance evaluation for the lower mobility parallel manipulators are still to be remained as two overwhelming challenges in the stage of conceptual design due to their geometric complexities. By using the screw theory, this paper explores the compliance modeling and eigencompliance evaluation of a newly patented 1T2R spindle head whose topological architecture is a 3-RPS parallel mechanism. The kinematic definitions and inverse position analysis are briefly addressed in the first place to provide necessary information for compliance modeling. By considering the 3-RPS parallel kinematic machine(PKM) as a typical compliant parallel device, whose three limb assemblages have bending, extending and torsional deflections, an analytical compliance model for the spindle head is established with screw theory and the analytical stiffness matrix of the platform is formulated. Based on the eigenscrew decomposition, the eigencompliance and corresponding eigenscrews are analyzed and the platform’s compliance properties are physically interpreted as the suspension of six screw springs. The distributions of stiffness constants of the six screw springs throughout the workspace are predicted in a quick manner with a piece-by-piece calculation algorithm. The numerical simulation reveals a strong dependency of platform’s compliance on its configuration in that they are axially symmetric due to structural features. At the last stage, the effects of some design variables such as structural, configurational and dimensional parameters on system rigidity characteristics are investigated with the purpose of providing useful information for the structural design and performance improvement of the PKM. Compared with previous efforts in compliance analysis of PKMs, the present methodology is more intuitive and universal thus can be easily applied to evaluate the overall rigidity performance of other PKMs with high efficiency.