Translational Joints Research Articles

Positioning Error Estimation Models for Horizontal-Distributed Prismatic–Universal–Universal Parallel Mechanism

Abstract In this paper, two models were proposed to estimate the positioning error of a 3-translational prismatic–universal–universal parallel kinematic mechanism. The two models were a kinematic error model (KEM) and a backpropagation neural network (BPNN) model, respectively. The KEM was constructed by incorporating three translational joint errors into the ideal kinematic model to describe the errors that occur during machining or assembly. Additionally, a sensitivity analysis was presented for each error parameter. The BPNN model was constructed to establish the relationship between the position of the end effector, the posture of each link, and the positioning error of the end effector using a neural network approach. Moreover, a hybrid method was proposed to decrease the final estimated residual error. The average errors of the KEM and BPNN models were 35% and 15% of the original error, respectively. The hybrid model reduced the final average error to less than 10% of its original value.

Nonsmooth dynamic modeling and simulation of spatial mechanisms with frictional translational clearance joints

This paper presents a nonsmooth dynamic approach of modeling and computation for spatial mechanism including spatial frictional translational joints (SFTJs) with small clearances. In this research, the dynamic formulation is derived in the Lie group setting, which leads to a coordinate-free and compact formulation. In the following, the normal contact interaction between the slider and guide is described by the complementarity relations between the constraint force in the normal direction. The tangent contact interaction in the SFTJ is characterized by the Coulomb’s friction law in the type of a set-valued map. Based on the horizontal linear complementarity problem (HLCP), the non-smooth dynamics can be established and calculated by combining the Lemke’s algorithm and the RK-MK time integration algorithm. Finally, A spatial crank-slider mechanism with SFTJs is shown as a numerical case. The simulation results demonstrate the correctness and effectiveness of the proposed method which can capture the nonsmooth dynamical behavior of the system.

Biomechanical comparison of static and dynamic cervical plates in terms of the bone fusion, tissue degeneration, and implant behavior

IntroductionUsing an anterior cervical fixation device in the anterior cervical discectomy and fusion (ACDF) has evolved to various systems of static and dynamic cervical plates (SCP and DCP). Dynamic cervical plates have been divided into three categories: the rotational (DCP-R), translational (DCP-T), and hybrid (DCP-H) joints. However, little studies have been devoted to systematically investigate the biomechanical differences of dynamic cervical plates.Materials and methodsThe biomechanical tests of load-deformation properties and failure modes between the SCP and DCP systems are implemented first by using the UHMWPE blocks as the vertebral specimens. The CT-based C2-C7 model simulates the strategies of cervical plate in ACDF surgery is developed with finite-element analyses. One intact, one SCP and two DCP systems are evaluated for their biomechanical properties of bone fusion and tissue responses.ResultsIn the situation of biomechanical test, The mean values of the five ACDSP constructs are 393.6% for construct stiffness (p < 0.05) and 183.0% for the first yielding load (p < 0.05) less than those of the SCP groups, respectively. In the situation of finite-element analysis, the rigid-induced ASD is more severe for the SCP, followed by the DCP-H, and the DCP-R is the least.Discussion and conclusionsConsidering the degenerative degree of the adjacent segments and osteoporotic severity of the instrumented segments is necessary while using dynamic system. The mobility and stability of the rotational and translational joints are the key factors to the fusion rate and ASD progression. If the adjacent segments have been degenerative, the more flexible system can be adopted to compensate the constrained mobility of the ACDF segments. In the situation of the osteoporotic ACDF vertebrae, the stiffer system is recommended to avoid the cage subsidence.

A Novel Method for Spatial Structural Kinematic Analysis

Kinematic analysis is the first task that needs to be solved for further real-life problems such as machine dynamics and durability, machine balancing, and optimization, chemistry, etc. Currently, there are many methods to analyze the kinematic problem, for instance: vector graphics method, vector-analytic method, or Dennavit-Hartenberg-Craig matrix method. Although each method has its advantages, they have mostly encountered difficulties in establishing equations associated with complicated spatial structures. This research proposed a novel method, entitled “'perpendicular projection method” to solve the problem of spatial structural kinematic analysis. This is an approximate solution method that combines the use of generalized coordinates and direction cosine matrices. With this method, the problem of kinematic analysis of spatial structures will be solved simply and easily by establishing connection equations as well as simulating the motion of spatial structures. This method was then applied in conducting the kinematic analysis of a spatial mechanism with 1 rotating joint (R), 1 ball joint (S), 1 translational joint (P), and one cylindrical joint (C). The calculated results, including the velocity, acceleration of generalized coordinates, angular velocity, angular acceleration of the links, velocity, and acceleration of the center of mass of the links, showed the efficiency of the proposed method.

Influence of two kinds of clearance joints on the dynamics of planar mechanical system based on a modified contact force model

This study takes the slider-crank mechanism with revolute joint and translational joint as the research object and studies the contact force model of the clearance joint and the influence of the hybrid clearance joints on the nonlinear dynamic behavior of the mechanism. A modified contact force model is established based on the simplified elastic oscillator model, which can be used as a normal force in clearance joint. In the new contact force model, the component n of the indentation depth can be arbitrarily selected and it can support the calculation of contact force for both fully elastic recovery, non-elastic recovery and fully inelastic recovery. Based on the LuGre friction model, the tangential friction model of the clearance joint is given. Thus, the normal force and tangential force during the dynamic contact of the clearance joint are formed. Combining Lagrange’s equations of the first kind with the modified normal force and tangential friction force, the dynamic equations of the multi-body system with clearance joints are established. The Baumgarte stabilization method is used to improve the numerical stability. The correctness of the dynamic prediction model in the mechanism with clearance joint is verified by experiment. The dynamic analysis of the slider-crank mechanism with mixed clearance joints shows that the revolute clearance joint has a greater influence on the mechanism than the translational clearance, and the revolute clearance joint plays a leading role in the dynamic response.

Error Analysis of a New Five-Degree-of-Freedom Hybrid Robot

The error analysis of the robot has a very practical significance for improving its accuracy. Therefore, this paper conducts an error analysis for a new five-degree-of-freedom hybrid robot designed to conduct responsible surface machining. Initially, the error sources of the hybrid robot were sorted out to determine the number of error sources. Then, the error mapping model of the hybrid robot is established by the closed-loop vector method and the first-order perturbation method. Based on the mapping property of the 6th-order velocity Jacobi matrix, the compensable and non-compensable error sources affecting the posture error at the end of the hybrid robot are separated. Finally, the error analysis of the separated error sources is carried out to study the effect of single error sources and multiple error sources coupled with the posture error at the end of the robot. The results show that among the individual error sources, the dynamic and fixed platform hinge position error has the most significant effect on the end of the robot; among the integrated posture errors after coupling multiple error sources, the position of the dynamic and fixed platform hinge position error and the translational joint initial position dominate; the analysis of the different trajectories also yields that the error introduced by each error source increases gradually with the increase of the end trajectory. When designing this hybrid robot, attention should be paid to the manufacturing and installation accuracy of the dynamic and fixed platform hinge point positions and the translational joint initial position.

Design Automation of a Two Scissors Lift

In this study, the design of a two scissors greenhouse lift trolley is considered. The maximum height of the platform from the ground is 3500 mm. A program developed in Visual BASIC to automate the design is introduced. The lift is modeled in SolidWorks (SW) and the finite element (FE) modal and static analyses are performed as an initial design first by using graphical user interface (GUI). The lift contains revolute joints and slider joints. A simply supported beam which has two revolute joints and a slider joint is studied to verify how to model the joints. Pim connectors are defined for revolute joints in SW-FE analysis. Spring connectors with very large values are defined between sliding faces in the normal direction for translational joints. The results obtained with solid finite elements in SW are compared with analytical results for the natural frequency and static analyses and it was observed that the results are in good agreement for the simply supported beam. &#x0D; An Excel file where a main sheet contains the list of the bodies and all the geometric values is created after the initial design. The Excel file also contains sheets for each body. Body sheets have all the dimensions in the sketches and features. The dimension values in the cells of the body sheets are defined by formulas related to the geometric values given in the main sheet. Kinematic, kinetic, and revision of the SW model are performed by the design automation program. The FE analyses are done by GUI and the results are evaluated. If the results are not satisfactory, the geometric values are changed in Excel file and the analyses are repeated. The final design is obtained by the iteration easily. The automation program and the procedure developed in this work can be extended other scissors lifts.

Bionic design of universal gripper for nursing robot with hybrid joints and variable Equivalent Link Length

Currently, most rehabilitation/nursing robots attach the human body to the end of the robot by ‘binding’ solution, which makes the operation complicated and greatly limits their applications. Therefore, it is necessary to study a universal gripper that can directly grasp human limbs as the end-effector of the robot. Inspired by the human hand, this paper proposes a bionic under-actuated gripper that imitates the structure of human hand. The concept of Equivalent Link Length (ELL) is proposed to optimize the envelope effect. And the structure with hybrid rotational and translational joints is proposed to increase gripping stiffness and to avoid the harmful component in the grip force. Theoretical analyses and experiments on envelope effect, force distribution and load capacity show that the propose gripper can grasp cylindrical (limb-shaped) objects with wide applicable size range, and also has a high load capacity. Furthermore, the gripper has the characteristic of almost constant force transfer ratio, which reduces the number of sensors required by the system. These results show that the gripper has the potential to be used in the nursing robot system.

Tribo-dynamic performances and vibration transmission of lubricated translational joints in marine engines

• A new tribo-dynamic model for lubricated translational joints in two-stroke marine engines is established to study its dynamic and lubrication performances. • The fit clearance and profile are investigated so as to reveal their influences on the tribo-dynamic performances. • The use of a quadratic profile is an effective way to form a stable wedge-shaped oil film and avoid unnecessary collisions. • The vibration energy of lubricated translational joints through an optimal quadratic profile is greatly reduced in each frequency band. In this paper, a new tribo-dynamic coupling model for lubricated translational joints in two-stroke marine engines is established to study its dynamic and lubrication performances. Dynamic responses of spatial rigid-flexible multi-body systems are solved by a unified absolute nodal coordinate formulation (ANCF). Mixed lubrication performances are described by the modified Reynolds equation and solved by the finite element method. According to the coupling model, the fit clearance and profile are investigated to uncover their influences on the tribo-dynamic performances. The results show that the use of a quadratic profile is an effective way to form a stable wedge-shaped oil film and avoid unnecessary collisions. An optimal quadratic profile of crosshead is suggested in the light of the above analysis, and its influence on the transmission characteristics of vibration signals in the joint is analyzed. It can be concluded that the vibration energy through the optimal profile is greatly reduced in each frequency band.

Spatial compliance modeling and optimization of a translational joint using corrugated flexure units

Compliant mechanisms with corrugated flexure units have been attracting increasing attention due to their large range of motion. However, most research has considered in-plane compliance, whereas the out-of-plane performance, which affects the load-carrying ability, has seldom been studied. In this paper, an analytical model for the spatial compliance of a corrugated flexure translational joint is formulated. The in-plane compliance of the corrugated flexure translational joint is modeled by the Maxwell–Mohr method and compliance matrix method. For the out-of-plane compliance, a modification method is proposed for the closed-form analytical solution based on a finite element analysis with shell elements. The corrugated flexure translational joint is further optimized to achieve a high in-plane and out-of-plane off-axis stiffness ratio, low first-order natural frequency, and large range of motion. Experiments were conducted to verify the effectiveness of the method.

Workspace and kinematic structure analysis of a 6-DOF Lambda parallel kinematic machine

This paper presents workspace and kinematic analysis of a parallel kinematic machine based on the Lambda mechanism. The considered parallel kinematic machine has six degrees of freedom (DOF), achievable with six actuated translation joints. The kinematic analysis includes the definition of every active part of the machine, as well as the definition of every active or passive joint used to connect machine parts. The mathematical model of the machine is created for the better understanding of the machine's operation. The proposed mathematical model of the machine includes inverse kinematic equations, whose solving presents the first step in workspace analysis. In this case, the offered parallel kinematic machine has six active-joint variables, and every active-joint variable is the result of one inverse kinematic equation. Verification of the inverse kinematic equations has been done analytically, using MatLab software and a CAD/CAM system. Workspace analysis, as one of the most important parameters of the parallel kinematic machine, presents the main topic of this paper. In this case two approaches to the workspace analysis are given. The first considered analysis is used to determine the achievable workspace of the machine, and the second analysis is used to determine the total orientation workspace of the machine. Polar coordinates are used to simplify the process of the workspace analysis.

DeepNet-Based 3D Visual Servoing Robotic Manipulation

The fourth industrial revolution (industry 4.0) demands high-autonomy and intelligence robotic manipulators. The goal is to accomplish autonomous manipulation tasks without human interventions. However, visual pose estimation of target object in 3D space is one of the critical challenges for robot-object interaction. Incorporating the estimated pose into an autonomous manipulation control scheme is another challenge. In this paper, a deep-ConvNet algorithm is developed for object pose estimation. Then, it is integrated into a 3D visual servoing to achieve a long-range mobile manipulation task using a single camera setup. The proposed system integrates (1) deep-ConvNet training using only synthetic single images, (2) 6DOF object pose estimation as sensing feedback, and (3) autonomous long-range mobile manipulation control. The developed system consists of two main steps. First, a perception network trains on synthetic datasets and then efficiently generalizes to real-life environment without postrefinements. Second, the execution step takes the estimated pose to generate continuous translational and orientational joint velocities. The proposed system has been experimentally verified and discussed using the Husky mobile base and 6DOF UR5 manipulator. Experimental findings from simulations and real-world settings showed the efficiency of using synthetic datasets in mobile manipulation task.

Numerical and experimental study on dynamic characteristics of planar mechanism with mixed clearances

Clearances in joints are unavoidable due to assemblage, manufacturing errors and wear, which will lead to poor dynamic performances and undesirable vibrations due to impact forces in clearance joints. In dynamics analysis of planar mechanical system, it is usually assumed that the revolute joint is planar joint with radial clearance. However, the axial clearance in the revolute joint and the clearance in the translational joint are ignored. In fact, even planar mechanical systems may exhibit out-of-plane motion due to misalignments. In this work, a planar slider-crank mechanism is used as the example to investigate the effects of mixed clearances on the dynamic responses of planar mechanical system considering radial and axial clearances in spatial revolute joint due to axis misalignment as well as clearance in planar translational joint. The dynamic responses of the planar slider-crank mechanism system with two spatial revolute clearance joints and a planar translation clearance joint are investigated using computational and experimental methodology. The mathematic model of the spatial revolute clearance joint and the planar translational clearance joint are presented. The clearance joints are considered as force constraints and the joint components of an imperfect joint with clearance are modeled as contact bodies. The normal contact force model of clearance joint is established using continuous contact force model. The friction effect is considered using modified Coulomb friction model. Different case studies are presented and discussed to investigate the effects of the mixed clearances on the dynamic responses of the planar slider-crank mechanism.

Spatial Compliance Modeling and Optimization of a Translational Joint Using Corrugated Flexure Units

Spatial Compliance Modeling and Optimization of a Translational Joint Using Corrugated Flexure Units

A Novel, Oriented to Graphs Model of Robot Arm Dynamics

Robotics is an interdisciplinary field and there exist several well-known approaches to represent the dynamics model of a robot arm. The robot arm is an open kinematic chain of links connected through rotational and translational joints. In the general case, it is very difficult to obtain explicit expressions for the forces and the torques in the equations where the driving torques of the actuators produce desired motion of the gripper. The robot arm control depends significantly on the accuracy of the dynamic model. In the existing literature, the complexity of the dynamic model is reduced by linearization techniques or techniques like machine learning for the identification of unmodelled dynamics. This paper proposes a novel approach for deriving the equations of motion and the actuator torques of a robot arm with an arbitrary number of joints. The proposed approach for obtaining the dynamic model in closed form employs graph theory and the orthogonality principle, a powerful concept that serves as a generalization for the law of conservation of energy. The application of this approach is demonstrated using a 3D-printed planar robot arm with three degrees of freedom. Computer experiments for this robot are executed to validate the dynamic characteristics of the mathematical model of motion obtained by the application of the proposed approach. The results from the experiments are visualized and discussed in detail.

Analysis and control of a Stewart platform as base motion compensators - Part I: Kinematics using moving frames

Kinematics and its control application are presented for a Stewart platform whose base plate is installed on a floor in a moving ship or a vehicle. With a manipulator or a sensitive equipment mounted on the top plate, a Stewart platform is utilized to mitigate the undesirable motion of its base plate by controlling actuated translational joints on six legs. To reveal closed loops, a directed graph is utilized to express the joint connections. Then, kinematics begins by attaching an orthonormal coordinate system to each body at its center of mass and to each joint to define moving coordinate frames. Using the moving frames, each body in the configuration space is represented by an inertial position vector of its center of mass in the three-dimensional vector space ℝ3, and a rotation matrix of the body-attached coordinate axes. The set of differentiable rotation matrices forms a Lie group: the special orthogonal group, SO(3). The connections of body-attached moving frames are mathematically expressed by using frame connection matrices, which belong to another Lie group: the special Euclidean group, SE(3). The employment of SO(3) and SE(3) facilitates effective matrix computations of velocities of body-attached coordinate frames. Loop closure constrains are expressed in matrix form and solved analytically for inverse kinematics. Finally, experimental results of an inverse kinematics control are presented for a scale model of a base-moving Stewart platform. Dynamics and a control application of inverse dynamics are presented in the part II-paper.

Формализм выписывания уравнения динамики манипуляторов

The problem of cumbersome equations of dynamics for manipulation systems of industrial robots (manipulators) with translational and rotational joints is solved. A new formalism for writing out the equations of dynamics of manipulators by using of guide cosines is proposed. Examples of writing out equations of dynamics of manipulators with guid cosines are given. The equations of dynamics in relative angles of rotation of bodies are obtained with the help of these guide cosines by applying their properties. These manipulators have from three to six degrees of freedom. In their equations of dynamics the geometric, kinematic, static and inertial parameters are explicit. The multipliers for accelerations and products of velocities are optimal in the sense of the minimum of arithmetic operations (additions and multiplications) that are needed for their calculations in the written out equations of dynamics. JS-code and method for verification of the equations of dynamics of manipulators written in analytical form are proposed. The problem is that when the equations are written out manually, errors and oversights in the intermediate entries and the final result are possible. Therefore it is necessary to check the results of writing out for absence of errors, i.e. to perform verification of formulas for calculation of constitutive equations of dynamics. To do this, we can use software designed to calculate the generalized driving forces of manipulators, i.e. to solve the first problem of dynamics. Such software is offered as a web-application, in which JS-function is used for verification of the equations of dynamics of manipulators. The method of verification of formulas to calculate the generalized forces of gravity and multipliers (coefficients) for generalized accelerations and products of generalized velocities in the equations of dynamics is developed. An example of verification of the equations of dynamics of the universal manipulator with six degrees of freedom in space is given. Aim. The aim of research is to develop a formalism for writing out the analytical form of the equations of the manipulators’ dynamics in the guide cosines of the principal axes of the coupled body coordinate systems, whose coefficients contain the minimum number of arithmetic operations. Research methods. The methods of research refer to vector and analytic mechanics of absolutely solid systems, to vector algebra, and to systems analysis and programming in scripting languages. Results. The results contain two proved statements, in which there are the formulas and the methodology that allow us to write manually the equations of dynamics of manipulators with three and six degrees of mobility both in guiding cosines and in generalized coordinates. In both cases it is impossible to simplify the obtained equations. Conclusion. The offered analytical types of the equations of dynamics occupy several lines. By the known classical formalisms (Lagrange, Appel, Nielsen, Newton-Euler, etc.) it is practically impossible to obtain similar results because of the large number of complex mathematical operations in their implementation and the cumbersomeness of the resulting formulas.

Space Detumbling Robot Arm Deployment Path Planning Based on Bi-FMT* Algorithm.

In order to avoid damage to service satellites and targets during space missions and improve safety and reliability, it is necessary to study how to eliminate or reduce the rotation of targets. This paper focused on a space detumbling robot and studied the space detumbling robot dynamics and robot arm deployment path planning. Firstly, a certain space detumbling robot with a ‘platform + manipulator + end effector’ configuration is proposed. By considering the end effector as a translational joint, the entire space detumbling robot is equivalent to a link system containing six rotating joints and three translational joints, and the detailed derivation process of the kinematic and dynamic model is presented. Then, ADAMS and MATLAB were used to simulate the model, and the MATLAB results were compared with the ADAMS results to verify the correctness of the model. After that, the robot arm deployment problem was analyzed in detail from the aspects of problem description, constraint analysis and algorithm implementation. An algorithm of robot arm deployment path planning based on the Bi-FMT* algorithm is proposed, and the effectiveness of the algorithm is verified by simulation.

Modeling of lubricated translational joints in rigid-partially flexible multibody systems and its application in two-stroke marine diesel engines

In this paper, a new tribodynamic model for the translational joints with clearance is proposed by coupling the mixed lubrication model and the rigid-flexible multibody system dynamic model. The lubrication behavior is described by the average Reynolds equation and the Greenwood-Tripp asperity contact theory. Under a unified framework of the absolute nodal coordinate formulation (ANCF), motion equations of the rigid-flexible multibody system are established. The assembled equations of tribodynamic model are solved by a stable and effective algorithm. An application example of a two-stroke marine diesel engine is then used to study the tribological and dynamic behaviors of the crosshead-guide translational joint with clearance. The results show that considering the elastic deformation of components will lead to more intense secondary motion and smaller local clearance, resulting in an oil film pressure distribution with great difference from the rigid body modeling.

An image-guided hybrid robot system for dental implant surgery.

Dental implant surgery is an effective method for remediating the loss of teeth. Robot is expected to increase the accuracy of dental implant surgery. However, most of them are industrial serial robot, with low stiffness and non-unique inverse kinematic solution, which may reduce the success rate and safety of robotic surgery. Compared to serial robot, parallel robot is more stiffness and has unique inverse kinematic. However, its workspace is small, which may not meet surgical requirements. Therefore, a novel hybrid robot dedicated to dental implant is proposed. The hybrid robot is composed of three translation joints, two revolute joints, and Stewart parallel manipulator. Stewart is used for performing surgical operation, while the joints are used for enlarging the workspace of Stewart. In order to ensure the safety of robot motion, physical human-robot interaction based on a variable admittance controller is applied in the robotic system. In addition, considering the small workspace of Stewart, an optimal model is proposed to minimize the joint movement of Stewart in adjusting the orientation of drill bit. Phantom experiments were carried out based on the prototype robot. In the experiments, the optimal model could be solved after 20 iterations, finding an ideal joint configuration. The proposed variable admittance controller could enhance comfort level effectively. The accuracy of robot is evaluated by angle, entry and exit deviation, which are 0.74 ± 0.25°, 0.93 ± 0.28mm, and 0.96 ± 0.23mm, respectively. The phantom experiments validate the functionality of the proposed hybrid robot. The satisfactory performance makes it more widely used in the practical dental implant surgery in the future.