Passive Prismatic Joint Research Articles

Design and Analysis of a Reconfigurable Hybrid Robot for Machining of Large Workpieces

Abstract Large workpieces are important components of core equipment in aerospace and other fields, where the machining mainly focuses on the surfaces and inner cavities. However, it may be unsuitable for existing machining robots to directly achieve integrated machining, that is, not only the high-precision surface machining but also the machining of different inner cavities in a limited space. To satisfy these machining requirements, a new reconfigurable hybrid robot (RHR) is proposed, called the 3PRR-3PSS-UPU RHR, for machining the surface and inner cavity of large workpieces (where P, P, R, S, and U stand for the actuated prismatic joint, passive prismatic joint, revolute joint, spherical joint, and universal joint, respectively). The proposed RHR consists of two parallel manipulators (PMs), in which one is a spatial 3PRR PM with one translational degree-of-freedom (DOF) and the other is a 3PSS-UPU reconfigurable PM (RPM) with different configurations of two rotational and one translational (2R1T) DOFs using locking equipment, which is the main advantage of the designed robot. The inverse kinematics and singularities of two PMs are analyzed. The stiffness performance of the spatial 3PRR PM is compared with that of a moving slider with one translational DOF. By evaluating the workspace and motion/force transmissibility, the kinematic performance of two PMs is presented using several local and global indices, followed by the dimensional optimization of link parameters. Based on the structural characteristics and excellent performance, it can be inferred that the 3PRR-3PSS-UPU RHR has great potential for machining large workpieces.

Quasi-Coordinates-Based Closed-Form Dynamic Modeling and Analysis for a 2R1T PKM with a Rigid–Flexible Structure

This work derives a closed-form dynamic model for a two rotational and one translational degrees-of-freedom (2R1T) parallel kinematic mechanism (PKM) with a hybrid rigid–flexible structure for force-control applications. Based on the three-prismatic-prismatic-spherical (3PPS) kinematic configuration of the 2R1T PKM and its zero-torsion motion characteristics, a symbolic formulation approach is proposed to establish closed-form kinematic models for both forward and inverse kinematics analysis. As the moving platform pose of the 2R1T 3PPS PKM can be readily determined by the three active prismatic joint variables and the three passive prismatic joint variables, these six joint variables are selected as the quasi-coordinates so as to systematically develop the closed-form dynamic model with a Lagrangian formulation, in which the stiffness and deformation of the three flexure-based passive prismatic joints are uniformly taken into consideration. Through eliminating the three passive prismatic joint variables based on the principle of virtual work and the relationships between the active and passive prismatic joint variables, a closed-form dynamic model for the 2R1T 3PPS PKM with a rigid–flexible structure is finally obtained. The correctness of the closed-form dynamic model was validated with the commercial dynamic simulation software. Utilizing the closed-form dynamic model, the effects of different flexure stiffness in driving directions on the required active joint force were investigated, which indicated that little flexure stiffness in driving directions is desired.

A simplified approach to develop fuzzy logic controller with disturbance estimator for control of a planar parallel (2PRP-PPR) motion platform

This work presents, a robust position tracking control of a 3-degrees of freedom 2PRP-PPR (P: Active Prismatic joint, P: Passive prismatic joint, R; Revolute joint) parallel motion mechanism. For controlling the motion of the defined platform, a simple method to develop a fuzzy logic controller called as robust single input fuzzy logic control (RSIFLC) algorithm is presented and used for the complex workspace trajectory tracking control problem with the existence of outside disturbances, variable uncertainties, and inner noises. The suggested control method comprises two sections: The first section considers a feed-forward expression to increase control action and a disturbance estimator to account for anonymous factors like outer disturbances and un-modeled dynamics. The second section employs single input fuzzy logic control as a feedback component to improve the system’s overall closed-loop stability. The experimental results demonstrate the superiority of the suggested control algorithm over traditional control schemes.

Design and manufacturing a novel screw‐in‐pipe inspection robot with steering capability

AbstractIn this article, a novel in‐pipe inspection robot is designed and manufactured in Kharazmi University KharazmPipeBot. This robot is able to move through any pipeline with a predefined diameter range with a variable pitch rate and report any desired data within the pipe with the aid of the installed camera. To achieve the highest stability of the robot through the pipe, the robot's movement is based on the screw locomotion protocol provided by the aid of its rotor and stator. A simple suspension is designed for three legs of the robot by installing a passive prismatic joint equipped with a spring for each leg to provide a smoother movement for the robot chassis. The main novelty of the robot is adding an extra controlling actuator for the robot which is the steer of the front wheels. This input can control the pitch rate of the robot movement and consequently the spiral track of the wheels can be actively managed. This importance lets us to bypass the probable obstacles attached to the inner wall of the pipes. A brief presentation of the robot model is delivered. Afterward, to verify the claimed novelties of the system, a prototype of the robot is manufactured in Kharazmi University and the efficiency of the robot is demonstrated by conducting some initial experimental tests. It is shown that the robot can move with a variable pitch rate through the wall and pass a detected obstacle accordingly.

Design and Analysis of a Stiffness-Enhanced 3-PPS Parallel Mechanism for Fault-Tolerant Underwater Vectored Thrusters

Vectored thrusters can significantly improve the maneuverability of underwater vehicles. However, due to the harsh underwater environment and severe working conditions, the thrust-vectoring device needs to be designed with high stiffness and high reliability. In this paper, a 3-degree-of-freedom (3-DOF) 3-PPS parallel mechanism is employed for the 2-DOF thrust-vectoring device, which has the advantages of high stiffness and a certain level of fault tolerance. The stiffness of the 3-PPS parallel mechanism is enhanced through employing additional passive prismatic joints. Based on the zero-torsion characteristics of the parallel mechanism, closed-form solutions are obtained for displacement analyses, and the orientation workspace of the moving platform under an actuation failure, i.e., one of the active prismatic joints is locked, is particularly investigated through an equi-volumetric partition method. To analyze the orientation workspace distribution under the actuation failure, the fault-tolerant workspace and the maximum inscribed workspace are defined. Furthermore, a new fault-tolerant index is proposed to evaluate the fault tolerance of the parallel mechanism. The proposed design analysis is validated through experiments on an engineering prototype of the parallel mechanism.

Workspace analysis of 3-DOF U-shape base planar parallel robotic motion stage using shape memory alloy restoration technique (SMART) linear actuators

The applications of lightweight planar parallel robotic manipulators are increasing enormously because of its various desirable characteristics such as low weight, lower inertia and higher stiffness. Higher accelerations and accuracies can be achieved in planar parallel manipulators. Also, shape memory alloy restoration technique (SMART)-based linear actuators are replacing huge and bulky linear actuators. This study presents the kinematic design of smart linearly actuated family of U-shape base planar parallel robotic manipulator. With the aid of solid modelling software, different available configurations were modelled and their workspace was analysed. The developed 3-DOF motion stages (18 unique configurations) were fabricated using fused deposition modelling process, and the top three configurations having higher workspace were further experimented. It is interesting to observe that the actual or experimental workspace of a particular manipulator configuration is further minimised from the predicted or feasible workspace. It is due to the presence of passive links, singularities, friction between the parts, heat dissipation, force distribution, stiffness, etc. The present study depicts the experimental workspace of the top three configurations, namely PPR-PRP-PRR, PRP-PPR-PRP and PRP-PPR-PRR. Since none of the experimental workspace observed is equal or higher than the model workspace, an efficiency loss in terms of workspace reduction was calculated to understand the acceptability of the configurations in different domains. Apart from the loss, the result disclosed that the actual workspace of all the manipulators was within the feasible workspace domain of mobile platform. The PPR-PRP-PRR manipulator was found to possess highest experimental workspace than other configurations. Note: P, P, and R refer to active prismatic, passive prismatic and passive revolute joints respectively.

Development and Workspace Analysis of Smart Actuation based Planar Parallel Robotic Motion Stage

The applications of light weight planar parallel robotic manipulators are increasing enormously because of their various desirable characteristics such as low weight, lower inertia, higher stiffness, energy efficiency etc. Higher accelerations and accuracies can be achieved using planar parallel manipulators (PPMs). Also, Shape Memory Alloy (SMA) based actuators are replacing huge and bulky actuators as SMA actuators provide higher work per unit mass as compared to other actuators and also undergoes silent actuation by simple actuation process. In the present study, three configurations (3PRP, PPR-2PRP and PRR-2PRP) of 3 degrees of freedom U-shaped base planar parallel robotic manipulator have been presented using SMA based smart actuators. The manipulator constitutes of one fixed base and one moving platform. The SMA spring acts as linear actuators mounted on the base which is connected to the end effector with the help of three limbs. A detailed experimental study was carried out to understand the workspace associated with each configuration. The movement of manipulators was investigated with the various combinations associated with the input SMA translation joints. And the study showed that the various configurations acquire different areas of workspace in the manipulator region. This study also shows the essence of SMA springs in PPMs for precise and accurate positioning of the end-effector and also its tracking ability for the development of future micro-motion stage. Note: P refers to Passive Prismatic Joint, R refers to Passive Revolute Joint and P refers to Active Prismatic Joint.

Kinematic Design of a 2R1T Robotic End-Effector With Flexure Joints

This paper focuses on the kinematic design issues for a three degrees-of-freedom (DOFs), i.e., two-rotational and one-translational (2R1T) end-effector to perform continuous contact operations, such as deburring, grinding, and polishing. The proposed end-effector design employs a 3-legged prismatic-prismatic-spherical (3-PPS) parallel mechanism due to its desired kinematic characteristics and dynamic behavior. As the 3-PPS parallel mechanism is featured with zero-torsion motion characteristic, the orientation of its moving platform can be always represented by a rotation about an axis parallel to its base platform plane. Through analysis of the rotation matrix of the moving platform, closed-form linear solutions for both forward and inverse displacement analyses are readily derived. Other critical design issues, such as passive prismatic joint displacement, parasitic motion, velocity, and singularity analyses, are addressed. For a specific dimension design of the 3-PPS parallel mechanism, the workspace analysis indicates that the proposed design can achieve a singularity-free $\pm 12 ^\circ \times \pm 12^\circ \times 25$ mm workspace. Furthermore, as the displacements of the passive prismatic joints are within 2.63mm, light-weight flexure-based prismatic joints are designed to replace the conventional heavy linear guides. The flexure-rigid structure of the 3-DOF 2R1T end-effector significantly improves the dynamic performance of the system. A prototype of the 3-DOF 2R1T robotic end-effector is designed and fabricated to verify the proposed design.

Serpentine and Rectilinear Motion Generation in Snake Robot Using Central Pattern Generator with Gait Transition

This paper contributes to the fabrication of a snake-like robot in which the motion can be achieved through active wheels. The robot is constructed in such a way that its size can be increased and decreased, as well as it can undulate into a sine wave-like shape. The snake robot with wheels consists of chain of links attached to each other with the help of the passive prismatic and revolute joints. A neural oscillator-based central pattern generator (CPG) algorithm is applied to the robot so that rhythmic serpentine as well as rectilinear motions can be generated in it. In addition, a novel smooth transition mechanics of robot motion, from stationary position to serpentine or rectilinear motion as well as transition between these two gaits, is also suggested in the paper. The working of the formulated CPG motion algorithm is realized through experimental setup equipped with a motion capture system as well as through simulations.

Pa<sup>2</sup> kinematic bond in translational parallel manipulators

Abstract. The Pa2 pair is composed of two intertwined articulated parallelograms connecting in parallel two links of a kinematic chain. This pair has two translational degrees of freedom leading to a translational plane variable with the position. Currently, the Pa2 pair appears in conceptual designs presented in recent papers. However, its practical application is very limited. One of the reasons for this can be the high number of redundant constraints it has. But, it has to be considered that most of them can be eliminated by replacing wisely the revolute joints by spherical joints. On the other side, the structure of the Pa2 pair contributes to increase the global stiffness of the kinematic chain in which it is mounted. Also, its implementation is a promising alternative to the problematic passive prismatic joints. In this paper, the Pa2 pairs are used in the design of a 3 − P Pa2 parallel manipulator. The potentiality of this design is evaluated and proven after doing the following analyses: direct and inverse kinematics, singularity study, and workspace computation and assessment.

4자유도 고속 병렬 로봇의 해석 및 설계

Delta parallel robots are now widely used for high-speed applications. However, typical Delta robots, such as ABB Flexpicker suffer from rotating axis with passive prismatic joint subjected to critical speed and so requiring careful maintenance. In this paper, a novel 4-DOF high-speed parallel robot with four legs is presented, which consists of three legs with 90 degree arrangement for translational motions and one remaining leg with rack & pinion gears for rotational motion. The inverse kinematics, velocity, acceleration, statics, and inverse dynamics have been analyzed. From the workspace analysis and inverse dynamics simulation for 0.43 sec cycle time, the 4-axis parallel robot prototype with 12kg payload has been designed. In the future research, computed torque control methods will be developed for the prototype.

A constrained assumed modes method for solution of a new dynamic equation for an axially moving beam

Flexible beams with prismatic joints have complicated differential equations. This complexity is mostly due to axial motion of the beam. In the present research, a horizontal flexible link sliding through a passive prismatic joint while attached to a rigid link of a robot moving in a vertical direction is considered. A body coordinate system is used which aids in obtaining a new and rather simple form of the differential equation without the loss of generality. To model the passive prismatic joint, the motion differential equation is written in a form of virtual displacement. Next, a solution method is presented for the lateral vibrations of the beam referred to as “constrained assumed modes method”. Unlike the traditional assumed modes method, in the proposed constrained assumed modes method, the assumed mode shapes do not each satisfy the geometrical boundary conditions of the point where passive prismatic joint is located. Instead, by writing additional constraint equations the combination of the assumed modes will satisfy the geometrical boundary conditions at location of the passive prismatic joint. Two case studies for the effect of axial motion on lateral vibration of the beam are presented. Approximate analytical results are compared with FEM results.

A unified neural oscillator model for various rhythmic locomotions of snake-like robot

This paper contributes to the understanding and implementation of different types of locomotion in a snake-like robot by using a proposed unified neural oscillator model as central pattern generator (CPG). A neural oscillator network is suggested so that several rhythmic movements can be generated in order to mimic the actual snake movements on land. The unified coupled neural oscillators in the network provide the desired orientation and displacement for the snake-like robot and they are applied to the different types of snake locomotion by just altering some of the parameters proposed in the paper. The design of snake-like robot, consisting of a series of wheeled links (links with active wheels) connected with each other using the passive prismatic and revolute joints, is also suggested in the paper. The passive prismatic joints facilitate the change of lengths of wheel-less links and in this way the robot can be elongated as well as shortened. In this paper the serpentine, rectilinear, and concertina types of actual snake locomotion are realized, through simulation studies, by using the unified neural oscillator model proposed for the snake-like robots.

Dynamics and vibration of a 3-PSP parallel robot with flexible moving platform

In this research, first an analytical model is presented for dynamic and vibration analysis of a 3-PSP parallel robot with a flexible moving platform. Next, the presented analytical model is solved using an approximate analytical method. The moving platform is assumed to be made of three Euler-Bernoulli beams joined together to form a star. Each of the three beams of the star slides through a passive prismatic joint. Then, three-dimensional vibration analysis of the flexible moving platform, star, with three passive prismatic joints is the main subject of the present research. Only vibration during free motion is considered. Therefore, it is assumed that only inertia forces of the star are the main source of its vibration. First, direct kinematics is used for acceleration analysis of the rigid robot and inertia forces are obtained. For dynamic modeling, the passive prismatic joints and junction point of the three beams are modeled using a new set of geometric constraints. Additionally, a previously developed constrained motion equation for a planar Euler-Bernoulli beam having a prismatic joint is further developed for the three beams of the star. Next, an approximate analytical solution method, called the “constrained assumed modes method”, is used for inverse dynamics and vibration analysis of the robot. Furthermore, the developed model can be used for direct dynamics analysis of the robot. Finally, several input trajectories and two different groups of mode shapes are considered to investigate the model efficiency. The results of the presented model are compared with the results of a commercial finite element method software.

Approximate analytical solution for vibration of a 3-PRP planar parallel robot with flexible moving platform

SUMMARYIn this research, using an approximate analytical method, vibration analysis of a 3-PRP (active prismatic—P, passive revolute—R, passive prismatic—P) planar parallel robot having a flexible moving platform is presented. A specific architecture of the 3-PRP parallel robot, also known as the ST (Star-Triangle) parallel robot, is considered. The moving platform of the robot, called the star, is assumed to be made of three flexible beams shaped like a star. For analytical modeling, each of the three beams of the star is assumed to be a discrete Euler–Bernoulli beam with a passive prismatic joint. Continuity equations at the center of the star are used to relate vibrations of the three beams. The vibration behavior of each beam is modeled using previously developed constrained motion equations for a planar Euler–Bernoulli beam having a prismatic joint. In this paper, previously presented “constrained assumed modes method” is further developed to solve the constrained motion equation for the ST parallel robot. The solution method is used to obtain the vibration of the robot for the inverse dynamics problem and simultaneously provides generalized constraint forces. Furthermore, the solution method can be used for the direct dynamics problem of the ST robot. Several input trajectories are considered to investigate the different behavior for the center of the star. For each of the trajectories, three different groups of mode shapes are considered and their vibrational responses are compared. In this research, for the first time, effects of the passive prismatic joint parameters such as mass, rotational moment of inertia, and its actual length are considered in an analytical model. Finally, the analytical solution and a FEM (Finite Element Method) software solution are compared.

An analytical model for vibration and control of a PR-PRP parallel robot with flexible platform and prismatic joint

An analytical solution for vibration of a parallel robot where its end-effector is flexible and has a passive prismatic joint(s) has not been presented before. In this research vibration analysis of a PR-PRP parallel robot using an analytical method is investigated. The PR-PRP parallel robot has two planar degrees of freedom and moves by means of two active prismatic joints. The robot moving platform is a flexible link with one passive revolute and one passive prismatic joint. First, the motion equation for a flexible link with the passive prismatic joint is developed. The motion equation is solved by employing an approximate analytical method called “constrained assumed modes method”. A time-variant constraint is written for the passive prismatic joint. The developed model allows for inclusion of the effect of physical length for the passive prismatic joint in contact with the moving platform on the vibration response of the system. For verification of the presented model and solution, three case studies are presented and results of the analytical solution are compared with results of a commercial finite element method software. For each case study, two different lengths for the passive prismatic joint are considered. Finally, active vibration control is performed for an applicable motion of the robot using the proportional-integral-derivative controller.

A 6-DOF Gait Rehabilitation Robot With Upper and Lower Limb Connections That Allows Walking Velocity Updates on Various Terrains

This paper presents a 6-DOF gait rehabilitation robot that allows patients to update their walking velocity on various terrain types and navigate in virtual environments (VEs) through upper and lower limb connections. This robot is composed of an upper limb device, a sliding device, two footpad devices, and a body support system. The footpad device on the sliding device generates 3-DOF spatial motions on the sagittal plane for each foot. This allows the generation of various terrain types for diverse walking training. The upper limb device allows users to swing their arms naturally through the use of a simple pendulum link with a passive prismatic joint. Synchronized gait patterns for this robot are designed to represent a normal gait with upper and lower limb connections. To permit patients to walk at will, this robot allows walking velocity updates for various terrain types by estimating the interaction torques between the human and the upper limb device, and synchronizing the lower limb device with the upper limb device. In addition, the patient is able to navigate in VEs by generating turning commands with switches located in the handles of the upper limb device. Experimental results using a healthy subject show that the user can update the walking velocity on level ground, slopes, and stairs through upper and lower limb connections. In addition, the user could navigate in the VEs with walking velocity updates and turning input command allowing various rehabilitation training modes. During a pilot clinical test, a hemiplegic patient could use the suggested gait rehabilitation robot with a slow walking speed. The rehabilitation plan was also suggested for the patient and the possible therapeutic effects of the suggested rehabilitation robot system are discussed.

S1108-1-2 パラレルメカニズムを用いた高速・高精度3次元座標計測システム : 第23報,冗長受動ジョイントを用いたキャリブレーション(パラレルメカニズムとその応用)

S1108-1-2 パラレルメカニズムを用いた高速・高精度3次元座標計測システム : 第23報,冗長受動ジョイントを用いたキャリブレーション(パラレルメカニズムとその応用)

3239 パラレルメカニズムを用いた高速・高精度3次元座標計測システム(第22報) : 冗長受動ジョイントを用いたキャリブレーション(S39-1 パラレルメカニズムとその応用(1),21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

3239 パラレルメカニズムを用いた高速・高精度3次元座標計測システム(第22報) : 冗長受動ジョイントを用いたキャリブレーション(S39-1 パラレルメカニズムとその応用(1),21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

Kinematic analysis and optimal design of 3-PPR planar parallel manipulator

This paper proposes a 3-PPR planar parallel manipulator, which consists of three active prismatic joints, three passive prismatic joints, and three passive rotational joints. The analysis of the kinematics and the optimal design of the manipulator are also discussed. The proposed manipulator has the advantages of the closed type of direct kinematics and a void-free workspace with a convex type of borderline. For the kinematic analysis of the proposed manipulator, the direct kinematics, the inverse kinematics, and the inverse Jacobian of the manipulator are derived. After the rotational limits and the workspaces of the manipulator are investigated, the workspace of the manipulator is simulated. In addition, for the optimal design of the manipulator, the performance indices of the manipulator are investigated, and then an optimal design procedure is carried out using Min-Max theory. Finally, one example using the optimal design is presented.