Screw Theory Research Articles

Dynamic response and time-variant reliability analysis of an eight-rod shock isolator

The operation of a warship is commonly affected by shock loads in different directions during sailing in a rough sea, which can decrease the precision of the shipboard equipment. To improve the shock resistance performance of the shipboard equipment, an isolator is usually installed to isolate it from the vibration of the ship deck. The paper proposes a method for dynamic response and time-variant reliability analysis of an eight-rod shock isolator (ERSI). ERSI has a novel symmetrical structure, which can improve the utilization of the isolation rods compared with the classical parallel mechanism. The isolator is modeled using Denavit-Hartenberg (D-H) convention and screw theory. Then, Duhamel integral is employed to derive the dynamic response to the isolator after decoupling the governing equation using the modal analysis method. Considering impacts of uncertain factors, this paper also presents a practical method for time-variant reliability analysis of ERSI. Finally, a discussion of the practical example of this method along with a detailed analysis to evaluate the efficiency of the proposed method is presented.

Improved design method for line gear pair based on screw theory

Improved design method for line gear pair based on screw theory

2PPaRR-2PPaRU: Design, analysis, and optimization of a new 3T1R parallel manipulator with rotational pitch motion

A new 3T1R parallel manipulator (PM) 2PPaRR-2PPaRU with rotational pitch motion is proposed in this paper. In such a mechanism, there are four limbs connected to the moving platform (MP) through several revolute joints and universal joints, and all actuated joints are prismatic joints with an axis along a vertical direction. Mobility and motion characteristics are verified by constraint screw theory. The inverse kinematic solutions and the singularity configurations are derived through kinematic analysis. Next, the workspace analysis and the connection between [Formula: see text] and the volume of the reachable workspace are performed. The local motion/force transmission index is selected to evaluate the local transmission performance of 2PPaRR-2PPaRU PM. Finally, the global motion/force transmission index and the volume of reachable workspace are considered simultaneously to optimize the structural parameters. The 2PPaRR-2PPaRU PM with improved local transmission performance and reachable workspace has been achieved after optimization.

Modeling of a wheeled humanoid robot and hybrid algorithm-based path planning of wheel base for the dynamic obstacles avoidance

PurposeMost of the conventional humanoid modeling approaches are not successful in coupling different branches of the tree-type humanoid robot. In this paper, a tree-type upper body humanoid robot with mobile base is modeled. The main purpose of this work is to model a non holonomic mobile platform and to develop a hybrid algorithm for avoiding dynamic obstacles. Decoupled Natural Orthogonal Complement methodology effectively combines different branches of the humanoid body during dynamic analysis. Collision avoidance also plays an important role along with modeling methods for successful operation of the upper body wheeled humanoid robot during real-time operations. The majority of path planning algorithms is facing problems in avoiding dynamic obstacles during real-time operations. Hence, a multi-fusion approach using a hybrid algorithm for avoiding dynamic obstacles in real time is introduced.Design/methodology/approachThe kinematic and dynamic modeling of a humanoid robot with mobile platform is done using screw theory approach and Newton–Euler formulations, respectively. Dynamic obstacle avoidance using a novel hybrid algorithm is carried out and implemented in real time. D star lite and a geometric-based hybrid algorithms are combined to generate the optimized path for avoiding the dynamic obstacles. A weighting factor is added to the D star lite variant to optimize the basic version of D star lite algorithm. Lazy probabilistic road map (PRM) technique is used for creating nodes in configuration space. The dynamic obstacle avoidance is experimentally validated to achieve the optimum path.FindingsThe path obtained using the hybrid algorithm for avoiding dynamic obstacles is optimum. Path length, computational time, number of expanded nodes are analysed for determining the optimality of the path. The weighting function introduced along with the D star lite algorithm decreases computational time by decreasing the number of expanding nodes during path generation. Lazy evaluation technique followed in Lazy PRM algorithm reduces computational time for generating nodes and local paths.Originality/valueModeling of a tree-type humanoid robot along with the mobile platform is combinedly developed for the determination of the kinematic and dynamic equations. This paper also aims to develop a novel hybrid algorithm for avoiding collision with dynamic obstacles with minimal computational effort in real-time operations.

Elasto-Dynamic Modeling of an Over-Constrained Parallel Kinematic Machine Using a Beam Model

This article deals with the development of a simple model to evaluate the first natural frequencies of over-constrained parallel kinematic machines (PKMs). The simplest elasto-dynamic models are based on multi-body approaches. However, these approaches require an expression of the Jacobian matrices that may be difficult to obtain for complex PKMs. Therefore, this paper focuses on the determination of the global mass and stiffness matrices of an over-constrained PKM in stationary configurations without the use of Jacobian matrices. The PKM legs are modeled by beams. Because the legs are connected to a moving platform and the mechanism is over-constrained, constraint equations between the parameters that model the deformation of each leg are determined according to screw theory. The first natural frequencies and associated modes can then be determined. It should be noted that the proposed method can be easily used at the conceptual design stage of PKMs. The Tripteor X7 machine is used as an illustrative example and is characterized experimentally.

Kinematics Analysis and Simulation of a Novel 3T Parallel Mechanism

Three translational (3T) degree-of-freedom (DOF) parallel mechanism is widely used in the industrial field because of its compact structure and excellent dynamic performance. Combined with the 3T parallel mechanism studied at this stage, a novel 3T parallel mechanism is proposed. Firstly, the DOF of the mechanism is analyzed by using the screw theory. Secondly, the position, velocity, and singularity of the mechanism are analyzed, and the workspace of the mechanism is analyzed through the positive position solution. Then, the trajectory planning in joint space and coordinate space is completed, and a common mathematical model of grasping trajectory is established. Thirdly, the kinematics simulation analysis of the mechanism is carried out. Finally, the prototype platform was built and the grasping experiment was carried out, which verified the rationality of the mechanism design and the correctness of the theoretical analysis.

Leg Configuration Analysis and Prototype Design of Biped Robot Based on Spring Mass Model

The leg structure with high dynamic stability can make the bionic biped robot have the inherent conditions to perform elastic and highly dynamic motion. Compared with the quadruped robot, the leg structure of the biped robot is more complex and has more degrees of freedom. This also complicates kinematic and dynamic modeling. In this paper, the kinematics model of a bionic biped robot is established. The leg configuration of the robot is a series parallel hybrid mechanism with five active joints and six passive joints. The mechanism is a spring mass model that interacts organically with the environment and mimics the characteristics of human walking well. By analyzing the topological configuration of leg mechanism, we use the screw theory to establish the forward and inverse kinematics models. Then, we build the prototype, and use a step gait to test the model and prototype. The research of this paper has obvious application significance for the design and iteration of biped robot prototype.

Different manipulation mode analysis of a radial symmetrical hexapod robot with leg\u2014arm integration

With the widespread application of legged robot in various fields, the demand for a robot with high locomotion and manipulation ability is increasing. Adding an extra arm is a useful but general method for a legged robot to obtain manipulation ability. Hence, this paper proposes a novel hexapod robot with two integrated leg—arm limbs that obtain dexterous manipulation functions besides locomotion ability without adding an extra arm. The manipulation modes can be divided into coordinated manipulation condition and single-limb manipulation condition. The former condition mainly includes fixed coordinated clamping case and fixed coordinated shearing case. For the fixed coordinated clamping case, the degrees of freedom (DOFs) analysis of equivalent parallel mechanism by using screw theory and the constraint equation of two integrated limbs are established. For the fixed coordinated shearing case, the coordinated working space is determined, and an ideal coordinated manipulation ball is presented to guide the coordinated shearing task. In addition, the constraint analysis of two adjacent integrated limbs is performed. Then, mobile manipulation with one integrated leg—arm limb while using pentapod gait is discussed as the single-limb manipulation condition, including gait switching analysis between hexapod gait and pentapod gait, different pentapod gaits analysis, and a complex six-DOF manipulation while walking. Corresponding experiments are implemented, including clamping tasks with two integrated limbs, coordinated shearing task by using two integrated limbs, and mobile manipulation with pentapod gait. This robot provides a new approach to building a multifunctional locomotion platform.

Novel Reconfigurable Spherical Parallel Mechanisms with a Circular Rail

The COVID-19 pandemic has placed unprecedented stress on the world healthcare system and demonstrated the need for modern automated robotic solutions for numerous medical applications. Often, robots that provide spherical motion of the end-effector are used in this area. In this paper, we discuss a spherical mechanism with a circular rail and provide several possible variations of the design: spherical robots with three or four legs and 4-DOF robots with an additional translational DOF, including a decoupled mechanism. The screw theory is used to analyze the mobility of the discussed mechanisms, and their advantages and drawbacks are discussed.

Type synthesis approach for the 2R1T compliant parallel mechanism with a suitable constrained branch

Abstract. In the aerospace field, the precision and stiffness for 2R1T (R denotes the rotation and the T denotes the translation) degree of freedom (DOF) space posture adjustment mechanisms are required. Compliant parallel mechanisms (CPMs) with a suitable constrained branch (SCB) have the advantages of high precision and high stiffness. Based on screw theory, a new type synthesis approach for a 2R1T compliant parallel mechanism with a suitable constrained branch is proposed. The proposed approach is an improvement of the freedom and constraint topology approach. It combines with other methods, including the rigid-body-replacement method, the principle of symmetry, etc. In order to obtain CPMs with a suitable constrained branch, the criterion for the type synthesis is presented. Using this proposed type synthesis approach, a series of CPMs is obtained. They include, but are not limited to, the existing typical 2R1T CPMs with a suitable constrained branch. Furthermore, it identifies the correctness and effectiveness of the approach by analyzing the DOF of the synthesized mechanism. This approach is also suitable for the type synthesis of 4, 5, and 6 DOF compliant parallel mechanisms with a suitable constrained branch.

Synthesis of asymmetric parallel mechanism with multiple 3-DOF motion modes

A method for designing asymmetric multi-mode parallel mechanism is proposed. Parallel mechanisms with 2R1T and 2T1R motion modes are synthesized by using displacement manifold theory. Based on the parallel mechanism, a kind of mechanism with hybrid variable DOF kinematic chain is proposed. The DOF characteristics of the mechanism in the process of motion mode transformation are analyzed by using screw theory, and the rationality of the selection of driving pairs in different motion modes is verified. The results show that the mechanism with hybrid variable DOF kinematic chain has 3R, 2T1R, and 2R1T motion modes. When the mechanism is in the general configuration of the four motion modes mentioned above, three driving pairs can control the mechanism. When the mechanism is in the transformation configuration having 2R2T or 3R1T instantaneous DOF, an additional auxiliary driving pair is needed to control the mechanism. The mechanism can realize multiple motion modes by using fewer driving pairs. It does not need to reassemble the mechanism when the motion mode is changed.

A novel reconfigurable parallel mechanism constructed with spatial metamorphic four-link mechanism

In this paper, a spatial metamorphic four-link mechanism (SMM) based on the metamorphic universal joint is proposed. By adjusting the axis position of the universal joint, three kinds of SMMs are constructed. Each kind of SMM has different bifurcation and metamorphic characteristics. Starting from the motion characteristics of each phase of SMM based on the screw theory, a reconfigurable hybrid limb is constructed by combining it with the series branch which can provide a constraint force and a constraint couple. The constraint changes of metamorphic hybrid limbs corresponding to different phases of SMM are analyzed. This leads to the design of a new type of reconfigurable parallel mechanism (RPM), in which the platform is connected to the base by three reconfigurable hybrid limbs. The results show that the performance of the RPM can be changed from 6 degrees of freedom (DOFs) to 5, 4, and 3 DOFs.

Constraint characteristics and type synthesis of two families of 1T2R parallel mechanism

AbstractPU- and P*U*-equivalent parallel mechanisms (PMs) are critical families of PMs with one translational and two rotational (1T2R) degree of freedoms and have always been a research hotspot among lower mobility PMs. However, researches on these two families of PMs remain to be inadequate, and existing types are few and uncomprehensive. In this study, first, general wrench systems of PU-equivalent are derived based on virtual-chain approach and screw theory, revealing its constraint characteristics under general configuration. Cause of one parasitic motion is put forward and general wrench systems of P*U*-equivalent PMs with one parasitic motion are obtained. In addition, constraint analysis has been carried out to figure out constraint characteristics of P*U*-equivalent PMs with three parasitic motions. Second, branch chains are divided by generating constraints, and their structures are synthesized based on the presented rules. Then, the process for type synthesis of PU-equivalent PMs and P*U*-equivalent PMs and a series of novel 1T2R PMs are attained based on this. Finally, a novel PU-equivalent PM, 2PRU-PRUPc, and a novel P*U*-equivalent PM with one parasitic motion, 2PRU-PUU PM, are analyzed, demonstrating the effectiveness of the proposed type synthesis method.

A Hybrid Mechanism-Based Robot for End-Traction Lower Limb Rehabilitation: Design, Analysis and Experimental Evaluation

Conventional lower-limb rehabilitation robots cannot provide in-time rehabilitation training for stroke patients in the acute stage due to their large size and mass as well as their complex wearing process. Aiming to solve the problems, first, a novel hybrid end-traction lower-limb rehabilitation robot (HE-LRR) was designed as the lower-limb rehabilitation requirement of patients in the acute stage, in this paper. The usage of (2-UPS + U)&(R + RPS)&(2-RR) hybrid mechanism and a mirror motion actuator had the advantages of compact structure, large working space and short wearing time to the HE-LRR. Then, the mobility of the HE-LRR was calculated and the motion property was analyzed based on screw theory. Meanwhile, the trajectory planning of the HE-LRR was carried out based on MOTOmed® motion training. Finally, the motion capture and surface electromyography (sEMG) signal acquisition experiments in the MOTOmed motion training were performed. The foot trajectory experimental effect and the lower-limb muscle groups activation rules were studied ulteriorly. The experimental results showed that the HE-LRR achieved good kinematic accuracy and lower limb muscle groups training effect, illustrating that the HE-LRR possessed good application prospects for the lower-limb rehabilitation of patients in the acute stage. This research could also provide a theoretical basis for improving the standardization and compliance of lower-limb robot rehabilitation training.

Vision-based measurement for decoupling identification of geometric errors of rotating axes for five-axis platform

In this paper, a method for identifying and decoupling geometric errors of rotation axes using vision measurement is proposed. Based on screw theory and exponential product formula, identification equations of position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs) of the rotation axes are established. The mapping relationships between the error twist and geometric errors are established. The error model provides the coupling mechanism of PDGEs and PIGEs. Furthermore, a progressive decoupling method is proposed to separate PDGEs and PIGEs without additional assumptions. The pose parameters, required for solving the identification equations, are obtained by visual measurement. Then, the error terms of PIGEs and PDGEs are determined. Lastly, the error calibration of the rotation axes is investigated, thus providing an average rotary table orientation error reduction of 28.1% compared to the situation before calibration.

High-precision modeling of CNCs\u2019 spatial errors based on screw theory

A method for establishing machine tool’s spatial error model is put forward based on screw theory, which is different from the traditional error modeling method. By analyzing the position relationship between the ideal coordinate vector and the actual coordinate vector jointly affected by linear errors and angular errors, a single-axis screw conversion matrix error expression is brought up based on screw theory. Meanwhile, the comprehensive spatial error model of the CNC machine tool is derived by considering the influence of the workpiece motion chain and the tool motion chain on the model. Further, to compensating spatial errors of CNCs, such screw theory-based model is embedded in the error compensation system by means of integration of a few specific application examples. And in order to evaluate the compensation effects, an integrated evaluation method of quantitative spatial diagonal calculation and MATLAB simulation is proposed. Application results show that the screw theory-based spatial error model of tool has a very substantial compensation effect, which makes the position error of the machine tool decreased by about 80%.

Twist and Finite Twist Analysis of 2upr-Spr Parallel Mechanism Based Upon Screw Theory

Twist and Finite Twist Analysis of 2upr-Spr Parallel Mechanism Based Upon Screw Theory

Static Force Analysis of a 3-DOF Robot for Spinal Vertebral Lamina Milling

In order to realize robot-assisted spinal laminectomy surgery and meet the clinical needs of the robot workspace, including accuracy in human–robot collaboration, an asymmetrical 3-DOF spatial translational robot is proposed, which can realize spinal laminectomy in a fixed posture. First, based on the screw theory, the constraint screw system of the robot was established, and the degree of freedom was derived to verify the spatial translational ability of the robot. Then, a kinematic model of the robot was established, and a static force model of the robot was derived based on the kinematic model. The mathematical relationship between the external force and the joint force/torque was obtained, with the quality of all links considered in the model. Finally, we modeled the robot and imported it into ADAMS to obtain the static force simulation results of the 3D model. The force error was approximately 0.001 N and the torque error was approximately 0.0001 N∙m compared with the simulation results of the mathematical model, accounting for 1% of the joint force/torque, which is acceptable. The result also showed the correctness of the mathematical models, and provides a theoretical basis for motion control and human–robot collaboration.

Spatial Planetary Movements for Multi-Axis EDM

Multi-axis electrical discharging machining (EDM) is the most commonly used manufacturing method for shrouded blisks. However, debris is difficult to be evacuated from a discharge gap, thus severely affecting the machining efficiency. Spatial planetary movements of a tool electrode can generate a non-uniform flow field in the discharge gap, promoting the evacuation of debris. This paper proposes a spatial planetary movement method for a feeding path of spatial line segments. Screw theory is used to derive the kinematics of a spatial planetary movement, and the coordinate increments of each axis in an interpolation period can be calculated. Then a multi-axis EDM machine can be controlled to drive a tool electrode to realize the spatial planetary movement. Machining experiments are carried out to explore the influences of the spatial planetary movement parameters on the machining performance of multi-axis EDM. Experiment results show that spatial planetary movements can improve the machining efficiency of multi-axis EDM, and the increase in the radius and speed of spatial planetary movements can further improve the machining efficiency. The machining efficiency can be increased by 51.62% and 50.44% respectively.

Investigation on the Basic Principles of Human-Machine Contact Force, Based on Screw Theory

Investigation on the Basic Principles of Human-Machine Contact Force, Based on Screw Theory