Screw Theory Research Articles

A novel 3-DOF translational parallel robot and its fuzzy controller design

In this paper, a novel three-degrees-of-freedom (3-DOF) parallel robot is designed, which can only move in three translational directions. It avoids the difficulty in the solution for forward kinematics of the parallel robot. The robot containing only lower pairs (P and R) has a simple mechanism. The characteristic that the parallel robot has only three translational degrees of freedom can be proved by the screw theory and the DOF can be got by the formula of calculating the DOF of space mechanism. The kinematics and workspace of the parallel robot is analyzed through calculation and simulation. In order to obtain better servo control performance, the PMSM fuzzy controller is designed. The analysis and simulation results show that the mechanism design of the parallel robot is reasonable, and the effect of fuzzy controller is better than the ordinary PID controller.

Link Lengths Optimization Based on Multiple Performance Indexes of Anthropomorphic Manipulators

How to determine the optimal link length parameters according to task requirements and constraints is a key problem in the design of anthropomorphic manipulators. Considering multiple performance indexes such as dexterity and end stiffness, this article presents a method on how to maximally improve the comprehensive motion performance of anthropomorphic manipulators by optimizing the link lengths. Firstly, the joint motion ranges of human arm are obtained through analyzing the motion mechanism and the motion forms. Then the kinematics model of manipulators with the optimal configuration is established by using screw theory, and a comprehensive evaluation index for the motion performance is proposed by considering the Jacobian matrix condition number, manipulability, and end stiffness. Taking the evaluation index as the objective function, the corresponding constraints and the optimization model are established to optimize the link lengths of manipulators with both flexibility and stiffness. Through comparative analyses, it can be seen that the global comprehensive performance index value of the optimized anthropomorphic manipulators increases by about 23.97%, and the motion performance is significantly improved.

Analysis of tilting table with parallel kinematics

The paper deals with the investigation of a workpiece moving unit with parallel kinematics. The subject of the study is the choice of the positions, installation location of actuator of the workpiece moving unit, table, how it affects the operation of the structure. This study is extremely important because the position of the actuators determines the functionality of the structure, i.e., we can predefine the position of the actuators so that the system can perform the desired movements. The possible installation locations of the actuators will be determined using combinatorics. Screw theory will be used to calculate the degree of freedom of the mechanism.

Designation and Multiobjective Optimization of a New Six‐DOF Haptic Device Based on Genetic Algorithm

This paper focuses on designation and multiobjective optimization of a new haptic device. A new six‐DOF hybrid haptic device has been designed combining series mechanism 3PRPaR and parallel mechanism ROBO_003.3PRPaR which is the positioning mechanism and ROBO_003 which is the directional mechanism. Screw theory was carried out to analyze the DOF of ROBO_003, aiming at the requirement performances of working space, stiffness, reverse drive, and output capacity of haptic device. Forward kinematics and inverse kinematics of the positioning mechanism were analyzed. To ensure the force transmission performance and compact structure, the evaluating indicator is dexterity and volume. Generalized coordinates as constraint condition, length of moving rod, and dexterity were chosen as the objective function. The parameters were optimized based on multiobjective optimization of the genetic algorithm. The paretooptimal solution set of the objective function was received. The results showed that the most suitable parameters are 0.502 rad. The optimized dexterity is 69% higher than the unoptimized, and the rod length is reduced by 6%.The research of this paper provides a theoretical basis for the designation of new haptic device.

Type Synthesis of 2T1R Planar Parallel Mechanisms and Their Moduling Development Applications

The two translational degrees-of-freedom (DOF) and one rotational DOF (2T1R) planar parallel mechanisms (PMs) have the characteristics of simple structures, simple kinematic and dynamic models, and ease of control and allow for a variety of application prospects. This paper concentrates on the derivations of the 5-DOF hybrid manipulators based on the synthesized mechanisms. To understand the effect of the constraint on the motion of a rigid body clearly, the method of reciprocal product between the wrench screw (constraint) and the twist screw (motion) is used and the relationships between the constraint and the motion of a rigid body are analyzed as well. The results are extended to the relationships between the limb constraint and the axes of limb joints. Then, limbs are divided into planar motion and spatial motion limbs in view of their motion characteristics, and some common limbs with constraint are listed. After that, based on the type synthesis method, a class of 2T1R planar PMs with common limbs is carried out. Meanwhile, some typical planar closed chains with two same limbs are obtained in the process of type synthesis. Finally, a 2T1R kinematically redundancy planar PM and two 2R1T spatial PMs are derived by making simple changes to the obtained mechanisms, and detailed derivations of three 5-DOF hybrid manipulators with the ability of processing spatial complex surface are given. Proved by the test parts, the accomplishment of deriving novel robot configurations with regard to expectant motion are quite valuable and practical.

Energy resource efficient designs of small-sized devices for recycled water cooling

Introduction. To use natural sources in rational way, plantsof continuous cooling of closed systems of recycling water supply are used. The paper presents designs of small-sized devices for recycling water cooling which are energy resource effective due to twisted motion of air flow, moving countercurrent to the cooled water. Heat and mass transfer is a nanotechnological process that occurs at the intermolecular level. Methods and materials. Countercurrent mini cooling towers are widely used in all industries,but there are some disadvantages, the main of which is the insufficient interaction time of the moving phases. Screw motion of air flow is created by the tangential supply of cooling air in the bottom part of cylindrical small-sized cooling tower. The rate of rotary motion decreases as air flow moves up in cooling towers, and vertical parameter of the rate – increases. Such scheme of the air flow motionmakes it possible to decrease average vertical parameter of the rate and to increase phases contact time. Laboratory research. To determine the technological and hydroaerothermal characteristics, as well as to estimate the efficiency of cooling recycled water, and to carry out mass-heat exchange at the intermolecular stagean experimental facility of small-sized cooling tower with twisted air flow has been developed. Conclusions. In accordance with the exponential law it is shown that the rotational component decreases at increasing height, and in accordance with the power law the vertical component increases component with the exponent ~1,79. It is determined that moisture content x and air temperature tv in the volume of the height of the sprinkler varies according to a power law, in particular for a screw cooling tower proportionally x ~ h0,83, t в ~ h1,25. It was determined that the coefficients of mass transfer βxv and heat transfer αv of a mini cooling tower with twisted air flow at the intermolecular level with equal irrigation densities are 20% higher than the coefficients of a mini cooling tower with counter-current flow. Also it has been determined experimentally a dependence of aerodynamics resistance coefficient of the twisted irrigator of the cooling tower on criterium Refor air flow, and it was determined that it decreases like Re–K2 as the exponent K2 varies in the range 0.114÷0.193 depending on the irrigation density

나선 운동을 이용한 랜덤 적재물의 도금특성

The chemical-plating quality of random-loaded small parts depends on the gap control between the parts in the bath. In this study, the plating characteristics for the screw motion of a basket in a bath were analyzed. This motion could be separated into parts for each, and the space for chemical reactions could be created, which improved its quality. The performance of the new technique was verified through experimental design and salt spray tests. The experimental results showed that the main factors that affected quality were temperature and plating solution concentration. In particular, the white rusting generated time of the screw motion method was longer than that of the conventional method.

Inverse solution of slave hand for single-port laparoscopic surgery robot based on hybrid Particle Swarm Optimization

Because of the particularity of the slave hand of the single hole laparoscopic surgery robot configuration, it cannot meet Pieper criterion, and its inverse kinematics solution cannot be obtained by traditional kinematics model. In order to solve the problems, the screw theory is used to establish the kinematics model for the slave hand of the single hole laparoscopic surgery robot. On this basis, the inverse kinematics is converted into a minimum solution problem. The optimal solution of each joint variable is obtained by using the hybrid particle swarm optimization (HPSO), and then the accuracy of pose matrix is analysed to verify the effectiveness of this method.

Geometric errors characterization of a five-axis machine tool through hybrid motion of linear-rotary joints

Position independent geometric errors (PIGEs) of rotary axes, which are caused by imperfections during assembly of machine tools, are proved to be one of the major error sources of a five-axis machine tool. In this paper, PIGEs’ characterization method through hybrid motion of linear-rotary axes using a double ball bar (DBB) is proposed. The coordinated motions involving the motion of a linear and rotary axes are designed, namely, the XC, YC, and ZB motion pairs. The comprehensive error model of the machine tool is established using the screw theory based on the machine tool topology. The asynchronization between the synthetized velocity of the spindle tool cup relative to the workpiece tool cup during the coordinated motions has been resolved based on optimal motion trajectories. The PIGEs are identified using the particle swarm optimization method and simulated using the comprehensive machine tool model. A compensation strategy of the identified errors is proposed using the machine inverse kinematics. The effectiveness of the proposed characterization method is proved by the compensation results.

Screw Theory Based Modeling Methodology of Horizontal Machining Center Volumetric Errors and Its Quantitative Validation

Screw Theory Based Modeling Methodology of Horizontal Machining Center Volumetric Errors and Its Quantitative Validation

Screw-in-screw fixation of fragility sacrum fractures provides high stability without loosening-biomechanical evaluation of a new concept.

Surgical treatment of fragility sacrum fractures with percutaneous sacroiliac (SI) screw fixation is associated with high failure rates. Turn-out is detected in up to 20% of the patients. The aim of this study was to evaluate a new screw-in-screw implant prototype for fragility sacrum fracture fixation. Twenty-seven artificial hemipelvises were assigned to three groups (n = 9) for instrumentation of an SI screw, the new screw-in-screw implant prototype, ora transsacral screw. Before implantation, a vertical osteotomy was set in zone 1 after Denis. All specimens were biomechanically tested to failure in upright position. Validated setup and test protocol were used for complex axial and torsional loading applied through the S1 vertebral body to promote turn-out of the implants. Interfragmentary movements were captured via optical motion tracking. Screw motions were evaluated by means of triggered anteroposterior X-rays. Interfragmentary movements and implant motions were significantly higher for SI screw fixation compared to both transsacral and screw-in-screw fixations. In addition, transsacral screw and screw-in-screw fixations revealed similar construct stability. Moreover, screw-in-screw fixation successfully prevented turn-out of the implant that remained during testing at 0° rotation for all specimens. From biomechanical perspective, fragility sacrum fracture fixation with the new screw-in-screw implant prototype provides higher stability than an SI screw, being able to successfully prevent turn-out. Moreover, it combines the higher stability of transsacral screw fixation with the less risky operational procedure of SI screw fixation and can be considered as their alternative treatment option.

A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

Performance Analysis and Optimization of a 6-DOF Robotic Crusher

Considering the complexity of multidimension parameters and the mechanical performance of a 6-DOF robotic crusher, a multiobjective optimization function based on the transmission index and condition number is established. As an important operation in the screw theory, the reciprocal product between the transmission wrench screw of an actuator and the output twist screw of the mantle assembly is used to represent the instantaneous power. The expression of transmission index is derived according to the principle that constraint wrench screws apply no work to the mantle assembly. It can be used as a criterion to evaluate the transmission performance. Then, based on the Jacobian matrix, the equation of condition number is constructed which provides a criterion for evaluating kinematic accuracy. Finally, the workspace and singularity of the 6-DOF robotic crusher are analyzed to verify the rationality of the optimized variables. The results show that the optimized structure can completely crush the material in the workspace and effectively avoid singularity, which provides a basis for practical application.

Configuration synthesis of linear foldable over-constrained deployable unit based on screw theory

According to a description of the topology structure of deployable antennas, this work proposes the configuration synthesis method of over-constrained deployable units on the basis of screw theory and conducts example analyses on the basis of an analysis method and certain design steps. First, the basics of screw theory are introduced in detail, and an over-constrained deployable unit is represented by a screw. Second, through over-constraint analysis, the kinematic pair configurations of the mechanism under over-constraint have been established. Third, according to the general process of the deployable unit with common over-constraints proposed in this paper, the example is analyzed in detail. Finally, the model is verified according to the obtained configuration synthesis results. The cubic deployable unit mechanism is obtained through 3D printing, and the folding function is tested to verify the correctness of the theoretical analysis, which can provide theoretical reference for the mechanism design of large deployable units.

A new method for type synthesis of parallel mechanisms using screw theory and features of genetic algorithms

The type synthesis is a fundamental phase in the design of parallel mechanisms. The type synthesis process consists of a systematic approach to generate all possible mechanical structures that are capable of performing a determined movement. The type synthesis presents two main steps: (1) generation of limbs and (2) assembly of parallel manipulators. There are basically three main approaches for type synthesis of parallel mechanisms: screw theory, lie group of rigid body displacements and evolutionary morphology. This paper presents a new method that combines screw theory and characteristics of genetic algorithms. Using the proposed method, it was generated new solutions of 3-DOF limbs (2R1T and 1R2T) for parallel manipulators.

Dynamics analysis of a novel in-wheel powertrain system combined with dynamic vibration absorber

Poor ride comfort is one of the drawbacks of in-wheel-drive electric vehicles (IWD-EVs). Structural schemes of the in-wheel powertrain system combining dynamic vibration absorber (IWP-DVA) can be applied to improve the ride comfort performance of the IWD-EVs without excessive useless weight. In this scheme, the in-wheel-drive motor is suspended as a mass block, thereby a dynamic vibration absorber (DVA) is mounted on the unsprung mass to absorb the vibration. This study developed a novel IWP-DVA involving a pair of symmetrical external-geared-slider-rocker (EGSR) mechanisms and a differential gear mechanism. In this paper, the novel IWP-DVA’s effectiveness in preventing the driving torque and the mass block’s travel from interacting was verified based on the static analysis of the single-EGSR mechanism, where the negative phenomena of stroke depletion due to the driving torque exists. For investigating the ride comfort responses and tuning the spring/damper parameters, a dynamics model of a quarter vehicle system equipped with the novel IWP-DVA was constructed by using screw theory and Lagrange method. After the selection of the DVA parameters, an analysis of the results of ride comfort tests showed that the novel IWP-DVA could improve the ride comfort with a sufficient stroke.

Design and optimization of solar tracker with U-PRU-PUS parallel mechanism

The solar tracker usually adopts the serial mechanism in application, which is greatly affected by the environment, and its load capacity and stability are limited. In order to address these issues, a new type of solar tracking device with U-PRU-PUS parallel mechanism was proposed. The U-PRU-PUS parallel mechanism was analyzed based on the screw theory, which shows that this mechanism has 2R degree of freedom and is decoupled. The direct and inverse kinematics of the parallel mechanism were derived and its singularity was analyzed based on the Jacobian algebras. Then the workspace of the parallel mechanism was obtained according to the boundary search algorithm. The adaptive genetic algorithm was used to search the optimal structure parameters of the parallel mechanism. The tracking range was improved by 4.6% and the stroke of the driving rod was shortened by 11.2% after optimization. A solar tracker prototype with the optimized parallel mechanism and its control system was built. The limit tracking position at sunrise and sunset was tested, which validated the feasibility of the designed mechanism and its tracking range. Through the solar tracking error tests, the performance of the proposed tracking mechanism can track the sun effectively.

Screw theory based method to formulate local Jacobian’ magnitude estimator contours for 6 DoF robots

Singularity prediction of Jacobian is inherently related to the design of any manipulator. Optimization of Jacobian is known to improve the joint rates and joint torques for the same set of end-effector twists and wrenches. Any mathematical entity which is an estimator of Jacobian can be used as a manifestation of the stated two schemes. It is required that online computation of Jacobian be implemented so that singular poses can be avoided and performance is maximized. We present an algorithm that relates to the determinant of the Jacobian for robotic manipulators. The algorithm developed is quicker to compute, and a strategy is developed to synthesize the local estimator contour. The contours change dynamically, henceforth optimal motor torques (in case of presence of interaction fields or system requiring force control) and optimal joint rates can be defined, depending on the control algorithm. The algorithm developed is independent of the structure of the matrix and is generalized to any six DoF manipulator structure used.

Configuration Design of Single-Loop Non-overconstrained Mechanism with Inactive Joints

In order to weaken the strict geometric constraint relationship between the axes of joints so as to reduce manufacturing/assembling errors of overconstrained mechanism, a configuration design methodology for single-loop non-overconstrained mechanism with inactive joints is proposed in this paper based on the screw theory. After completing analysis of degrees of freedom, the design principle and corresponding process of single-loop non-overconstrained mechanism with inactive joints are presented. By introducing two inactive R (R: single-degree-of-freedom revolute joint) joints to an active R joint of Goldberg overconstrained mechanism, the corresponding Goldberg non-overconstrained mechanism is obtained. It is verified that the velocities of two inactive joints in the Goldberg non-overconstrained mechanism are zero via investigating motion screws of branches. By further solving input and output kinematic parameters of Goldberg non-overconstrained mechanism, it is discovered that the overconstrained mechanism and corresponding non-overconstrained mechanism have the identical input–output relationship. Above results confirm that the overconstrained mechanism and its non-overconstrained counterpart with inactive joints are completely equivalent kinematically, which thereby demonstrate fully correctness of the configuration design principle and method of single-loop non-overconstrained mechanism proposed in this paper.

Multi-Loop Rover: A Kind of Modular Rolling Robot Constructed by Multi-Loop Linkages

Abstract This paper proposes a new kind of modular rolling robot called multi-loop rover (MLR), which is essentially a multi-loop linkage that is able to roll and switch its rolling directions. For ease of rolling, the MLR retains a multi-loop topological structure composed of a number of strut and node modules. First, the modular design and assembling method are introduced to construct an MLR. Then, the mobility is analyzed based on screw theory, and a brief formula is presented to calculate the degree-of-freedoms of the robot. The results show that all node modules only have translational motions, which can significantly reduce the complexity of kinematics. The forward and inverse kinematics are conducted to show the deformation properties. Based on the kinematic rolling principle, the morphing strategies for rolling and turning functions are developed. Finally, a physical prototype is manufactured and a serial of experiments are carried out to verify the proposed method.