Passive Spherical Joint Research Articles

A Novel Walking Parallel Robot for On-Structure Three-Axis Machining of Large Structures

Abstract This paper presents a novel walking hybrid-kinematics robot having three degrees-of-freedom for on-structure machining of large structures. A symmetric 3PRRR parallel mechanism having maximally regular properties is used to provide three-dimensional translational manipulation. Three attachment pads are connected to the base of the parallel mechanism through passive spherical joints, whereas multiple attachment pads are connected to the moving platform of the parallel mechanism. A machining task is performed by using a retractable tool holder attached to the parallel mechanism's moving platform. Two walking patterns, namely rotational and translational walking patterns, are defined for the robot. The kinematics of the manipulation and walking motions was derived and simulated. Several schemes to perform multi-step walking motions were also discussed. Subsequently, using an energy-based approach with the Stribeck friction model, the robot's dynamics was modeled and experimentally verified. Finally, an implementation of the robot to perform an on-structure machining task is discussed.

A Reconfigurable Parallel Robot for On-Structure Machining of Large Structures

This paper presents a novel walking hybrid-kinematics robot that can be reconfigured to have three, five, and six degrees of freedom (DOFs) for adsorption machining of large structures. A symmetric 3PRPR or 3PRRR parallel mechanism with three translational (3T) DOFs is used to perform three-axis machining tasks. Three attachment pads connected to passive spherical joints are used to attach the robot to the surface of a large structure. Two or three rotational degrees of freedom can be added to the robot to adapt to a large structure’s irregular surface geometry and perform five- or six-axis machining tasks. This is achieved through modular reassembly or joint locking that reconfigures the robot from a three-DOF robot to a five- or six-DOF robot. A serial module providing two rotational DOFs can be added to the 3T parallel mechanism to provide five DOFs. A parallel module, namely 3SPR or 3SU mechanism, can be added to the 3T parallel mechanism to provide six DOFs. The mobility, pose kinematics, differential kinematics, singularities, and workspace of the 3SPR and 3SU parallel mechanisms alone and combined with the 3T mechanism are discussed in this paper. It is shown that the singularities of the mechanism can be easily avoided by making the moving platform of the 3SPR or 3SU mechanism smaller than the base, limiting the range of some joints, and having an appropriate length of the links. Furthermore, a method to optimize the workspace of the mechanism was also discussed.

Kinematic and mechanical modelling of a novel 4-DOF robotic needle guide for MRI-guided prostate intervention

Traditionally ultrasound-guided biopsy has been used to diagnose prostate cancer despite of its poor soft tissue contrast and frequent false negative results. Magnetic Resonance Imaging (MRI) has the advantage of excellent soft tissue contrast for guiding and monitoring prostate biopsy. However, its working area and access in the confined MRI bore space limit the use of interventional guide devices including robotic systems. To provide robotic precision, greater access, and compact design, we designed a novel robotic mechanism that can provide four degrees of freedom (DOF) manipulation in a compact form comparable to size of manual templates. To develop the mechanism, we established a mathematical model of inverse and forward kinematics and prototyped a proof-of-concept needle guide for MRI guided prostate biopsy. The mechanism was materialized using four discs that house small passive spherical joints that can be moved by rotating the discs consisting of grooved profile. With an initial needle insertion angle range of ±15⁰, we identified mathematical and kinematic parameters for the mechanism design and fabricated the first prototype that has dimension of 40 × 110 × 180 mm3. The prototype demonstrated that the unique robotic manipulation can physically be delivered and could provide precise needle guidance including angulated needle insertion with higher structural rigidity.

Deformable One-Dimensional Object Detection for Routing and Manipulation

Many methods exist to model and track deformable one-dimensional objects (e.g., cables, ropes, and threads) across a stream of video frames. However, these methods depend on the existence of some initial conditions. To the best of our knowledge, the topic of detection methods that can extract those initial conditions in non-trivial situations has hardly been addressed. The lack of detection methods limits the use of the tracking methods in real-world applications and is a bottleneck for fully autonomous applications that work with these objects. This paper proposes an approach for detecting deformable one-dimensional objects which can handle crossings and occlusions. It can be used for tasks such as routing and manipulation and automatically provides the initialization required by the tracking methods. Our algorithm takes an image containing a deformable object and outputs a chain of fixed-length cylindrical segments connected with passive spherical joints. The chain follows the natural behavior of the deformable object and fills the gaps and occlusions in the original image. Our tests and experiments have shown that the method can correctly detect deformable one-dimensional objects in various complex conditions.

Static Force-Based Modeling and Parameter Estimation for a Deformable Link Composed of Passive Spherical Joints With Preload Forces

To balance the contradiction between higher flexibility and heavier load bearing capacity, we present a novel deformable manipulator which is composed of active rigid joints and deformable links. The deformable link is composed of passive spherical joints with preload forces between socket-ball surfaces. To estimate the load bearing capacity of a deformable link, we present a static force-based model of spherical joint with preload force and analyze the static force propagation in the deformable link. This yields an important result that the load bearing capacity of a spherical joint only depends on its radius, preload force, and static friction coefficient. We further develop a parameter estimation method to estimate the product of preload force and static friction coefficient. The experimental results validate our model. 80.4% of percentage errors on the maximum payload mass prediction are below 15%.

A Novel Robotic Platform for Aerial Manipulation Using Quadrotors as Rotating Thrust Generators

We propose a novel robotic platform for aerial operation and manipulation, a spherically connected multiquadrotor (SmQ) platform, which consists of a rigid frame and multiple quadrotors that are connected to the frame via passive spherical joints and act as distributed rotating thrust generators to collectively propel the frame by adjusting their attitude and thrust force. Depending on the number of quadrotors and their configuration, this SmQ platform can fully (or partially) overcome the issues of underactuation of the standard multirotor drones for aerial operation/manipulation (e.g., body-tilting with sideway gust/force, dynamic interaction hard to attain, complicated arm–drone integration, etc.). We present the dynamics modeling of this SmQ platform system and establish the condition for its full actuation in SE(3). We also show how to address limited range of spherical joints and rotor saturations as a constrained optimization problem by noticing the similarity with the multifingered grasping problem under the friction-cone constraint. We then design and analyze feedback control laws for the S3Q and S2Q systems as a combination of high-level Lyapunov control design and low-level constrained optimization and show that the (fully actuated) S3Q system can assume any trajectory in SE(3), whereas the S2Q system in $\Re^3\, \times$ S $^2$ with its unactuated dynamics is still internally stable. Experiments are also performed to show the efficacy of the theory.

Efficient computation of motion error of parallel robots with joint clearances based on joint force model

This paper proposes a method to compute positioning error of a parallel mechanism having passive spherical joints with clearances in motion without numerical integration nor iterative calculation. A model of passive spherical joints, in which the relationship between the relative displacement between the joint elements and the joint force obtained without taking the clearance into consideration is defined, is presented. Based on this model and the principle of virtual work, a procedure to calculate the output position error caused by joint clearance is proposed. Experiments for a DELTA parallel robot with joint clearances were conducted to evaluate the effectiveness of the proposed method comparing the measured output position error with the computational results. The applicability of the proposed method was discussed with a time variable for the relative displacement of the joint elements to converge, when the joint reaction force changes, defined as stabilization time. An index, representing an approximation of the stabilization time, was defined under consideration of rebounding and sliding motions between joint elements. The validity of the index was confirmed by investigating the correspondence between calculated index and the stabilization time obtained with experiments when changing the acceleration of the robot.

A heliostat based on a three degree-of-freedom parallel manipulator

In this paper, we propose a three-degree-of-freedom spatial parallel manipulator to track the sun in central receiver tower based concentrated solar power systems. The proposed parallel manipulator consists of three ‘legs’ each containing a passive rotary(R) joint, an actuated sliding or prismatic (P) joint and a passive spherical (S) joint and is known in literature as the 3-RPS manipulator. In contrast to existing serial mechanisms with two degrees-of-freedom, firstly it is shown that the extra actuator and enhanced mobility helps in reducing spillage losses and astigmatic aberration. Secondly, due to the three points of support, the beam pointing errors are less for wind and gravity loading or, alternately, the weight of the supporting structure to maintain desired deflections of the mirrors are significantly lower. Finally, the linear actuators used in the parallel manipulator do not require the use of large, accurate and expensive speed reducers. In this paper, we model the 3-RPS manipulator and derive the kinematics equations which give the motion of the linear actuators required to track the sun and reflect the incident solar energy at a stationary target at any time of the day, at any day of the year and at any location on the surface of the Earth. Finite element analysis is used to determine an optimized design which can reduce the weight of the supporting structure by as much as 60% as compared to the existing tracking mechanisms. A proportional, integral plus derivative (PID) control strategy using a low-cost processor is devised and a detailed simulation study is carried out to show that the proposed parallel manipulator performs better compared to the current tracking algorithms. Finally, a prototype of the parallel manipulator is manufactured and it is demonstrated that it is capable of performing autonomous sun tracking with the above mentioned advantages.

A Novel Three-Loop Parallel Robot With Full Mobility: Kinematics, Singularity, Workspace, and Dexterity Analysis

A novel parallel robot, dubbed the SDelta, is the subject of this paper. SDelta is a simpler alternative to both the well-known Stewart–Gough platform (SGP) and current three-limb, full-mobility parallel robots, as it contains fewer components and all its motors are located on the base. This reduces the inertial load on the system, making it a good candidate for high-speed operations. SDelta features a symmetric structure; its forward-displacement analysis leads to a system of three quadratic equations in three unknowns, which admits up to eight solutions, or half the number of those admitted by the SGP. The kinematic analysis, undertaken with a geometrical method based on screw theory, leads to two Jacobian matrices, whose singularity conditions are investigated. Instead of using the determinant of a 6 × 6 matrix, we derive one simple expression that characterizes the singularity condition. This approach is also applicable to a large number of parallel robots whose six actuation wrench axes intersect pairwise, such as all three-limb parallel robots whose limbs include, each, a passive spherical joint. The workspace is analyzed via a geometric method, while the dexterity analysis is conducted via discretization. Both show that the given robot has the potential to offer both large workspace and good dexterity with a proper choice of design variables.

A geometric approach for forward kinematics analysis of a 3-SPS/S redundant motion manipulator with an extra sensor using conformal geometric algebra

This paper proposes a geometric approach for forward kinematics analysis of a 3-SPS/S redundant motion mechanism using conformal geometric algebra (CGA). The forward kinematics of a parallel kinematic mechanism is generally very complicated and difficult to analyze. The proposed geometric method is useful because it provides simple, fast, and complete solutions to the problem and helps determine the relationship between the joints and end-effector without an iterative process. Thus, we introduce a geometric approach using CGA in an intuitive, stepwise fashion. We also use an extra sensor to provide more positional information, thereby allowing a unique solution to be selected geometrically from among the multiple solutions found using the geometric approach. In the mechanism considered herein, three identical legs linked by prismatic actuators are attached to a moving platform and to the base by two passive spherical joints. A passive leg is present at the center of the mechanism; it connects the center of the base to the platform, constraining the platform’s movement. The added components constrain the movement of the platform, making it possible to analyze the mechanism using a geometric approach. Herein we present performance comparisons that validate use of the proposed approach in real-time applications and demonstrate its low computational load.

Control and Motion Planning of a Nonholonomic Parallel Orienting Platform

An orienting platform is a mechanism which allows rotation of a spatial object without translational motion of that object. In this work, we study a parallel platform with one passive nonholonomic spherical joint and two series of spherical, actuated prismatic and universal joints (the platform is also known in literature as an (nS)-2SPU wrist). To solve the control and motion planning problems, an analytic approach is used. The design of practical stabilization and tracking algorithm is based on transverse functions and a method for motion planning respecting mechanical singularities is derived from endogenous configuration space approach. It is shown that the system is controllable and locally equivalent to the chained form system. Then, the stabilization, tracking, and motion planning algorithms are proposed. Results are verified with computer simulations. A combination of the open-loop motion planning algorithm and the closed-loop tracking provide a tool for designing a motion planning algorithm respecting mechanical singularities and robust to input disturbances.

Development of a new 4-DOF endoscopic parallel manipulator based on screw theory for laparoscopic surgery

Development of rigid manipulators for Minimally Invasive Surgery (MIS) becomes essential to replace wire driven manipulators which are problematic due to possible cutting of the wire during the surgery. In this paper, a 4-DOF dexterous endoscopic parallel manipulator for MIS is designed and implemented. The manipulator is developed based on the concept of virtual chain and screw theory. The manipulator consists of four links; two links are 2-PUU (each leg consists of one active prismatic joint and two passive hook joints); the other two links are 2-PUS (each leg consists of one active prismatic join, one passive hook joint and one passive spherical joint). The inverse and forward kinematics solutions are derived analytically and numerically, respectively. The singularity analysis is investigated using screws algebra. The manipulator workspace is obtained using MATLAB software. The known problem of limited bending angles found in previous existing surgical manipulators was solved as the proposed manipulator can reach ±90° in any direction. The proposed surgical manipulator is designed, manufactured and tested successfully. The system model utilizing PID and PI controllers has been built using MATLAB software. Co-simulation using ADAMS/MATLAB software is implemented to validate the achieved bending angles and the proposed tracking control. The results show that the performance of the tracking control is satisfactory since the tracking error is about 2.5%.

Motion capability analysis of a quadruped robot as a parallel manipulator

This paper presents the forward and inverse displacement analysis of a quadruped robot MANA as a parallel manipulator in quadruple stance phase, which is used to obtain the workspace and control the motion of the body. The robot MANA designed on the basis of the structure of quadruped mammal is able to not only walk and turn in the uneven terrain, but also accomplish various manipulating tasks as a parallel manipulator in quadruple stance phase. The latter will be the focus of this paper, however. For this purpose, the leg kinematics is primarily analyzed, which lays the foundation on the gait planning in terms of locomotion and body kinematics analysis as a parallel manipulator. When all four feet of the robot contact on the ground, by assuming there is no slipping at the feet, each contacting point is treated as a passive spherical joint and the kinematic model of parallel manipulator is established. The method for choosing six non-redundant actuated joints for the parallel manipulator from all twelve optional joints is elaborated. The inverse and forward displacement analysis of the parallel manipulator is carried out using the method of coordinate transformation. Finally, based on the inverse and forward kinematic model, two issues on obtaining the reachable workspace of parallel manipulator and planning the motion of the body are implemented and verified by ADAMS simulation.

Leg kinematic analysis and prototype experiments of walking-operating multifunctional hexapod robot

This paper presents kinematic analysis of a 3-degree of freedom parallel mechanism for hexapod walking-operating multifuctional robot. Each leg of the robot consists of three limbs: universal joint – prismatic joint chain (1-UP) and universal joint – prismatic joint – spherical joint chain (2-UPS) and at the end of the leg there is passive spherical joint to adjust to the uneven ground. In this paper, first the forward kinematic model is built and it shows that the model has close-form solution. Then the work space is discussed in which the robot feet trajectories can be projected. It can be shown that the current trajectories of the feet only take very small work space. After that force analysis is performed and the results show that the payload capability of the mechanism is very high. Experiments of the prototype show that the robot can walk easily with more than 150 kg loads while the step size is more than 0.5 m.

Forward Dynamics of the 6-PUS Parallel Manipulator Based on the Force Coupling and Geometry Constraint of the Passive Joints

This paper presents a simplified approach for the forward dynamics of the 6-PUS parallel manipulator. In the proposed method, the parallel manipulator is divided into the limb parts and the platform part at the passive spherical joints. For both parts, the equivalent dynamic equations related to the passive joints are obtained based on the transformation principles of dynamics between different spaces. Then, in acceleration level, the dynamic model for both parts can be rewritten in the form of linear equations on the generalized constraint forces and the linear accelerations of the passive joints on the condition that the state (position and velocity) of the manipulator is specified. According to the force coupling and geometry constraint of passive joints, the closed form solution for the generalized constraint forces can be derived readily from the linear equations combined by the separated parts. In the level of position and velocity, task variables of the manipulator, namely the position and orientation of the moving platform, are chosen as the system's generalized coordinates, which results in the utilization of the inverse kinematics for the state transformation between the workspace and the passive joints space. Consequently, by virtue of the obtained constraint forces, the dynamics of the manipulator can be replaced by a single free rigid body (the platform) with specified external forces provided by the environment through the end-effector and the limbs through the passive spherical joints, respectively. At last, some numerical results are provided and compared to validate the correctness and effectiveness of the proposed approach.

125666 FORWARD DYNAMICS OF THE 6-PUS PARALLEL MANIPULATOR BASED ON THE FORCE COUPLING AND GEOMETRY CONSTRAINT OF THE PASSIVE JOINTS(Robotics and Mechatronics)

This paper presents a simplified approach for the forward dynamics analysis of the 6-P__-US parallel manipulator, as shown in figure.1, based on the force coupling and geometry constraint of the passive spherical joints. In the proposed method, the parallel manipulator is divided, at the passive joints, into the limbs parts and the platform part. And for both kinds of parts, the equivalent dynamic equations relating to the decomposing joints are obtained based on the transformation principles of dynamic equations between different spaces. Then, in the acceleration level, the dynamic models for both parts can be rewritten in the form of linear equations on the generalized constraint forces and the accelerations of the passive joints on the condition that the state (position and velocity) of the manipulator is specified. Thus, according to the force coupling and geometry constraints of the passive joints, the closed form solution for the generalized constraint forces can be derived readily from the linear equations system combined by the separated parts. Additionally, in the position/velocity level, the task space variables of the manipulator (the position and orientation of the platform) are chosen as the system generalized coordinates, which only results in the utilization of the inverse kinematics for the state transformation between the workspace and the passive joints space. Hence, by virtue of the constraint forces obtained from the above linear equations, the dynamic model of the parallel manipulator can be replaced by a single free rigid body (the platform) with specified external applied forces, provided by the environment through the end-effector and the limbs through the passive spherical joints, respectively. In the end, some numerical results are provided and compared to validate the correctness and effectiveness of the proposed approach.

Triple Stance Phase Displacement Analysis With Redundant and Nonredundant Sensing in a Novel Three-Legged Mobile Robot Using Parallel Kinematics

This paper presents the forward and inverse displacement analysis of a novel three-legged walking robot Self-excited Tripedal Dynamic Experimental Robot (STriDER) in its triple stance phase. STriDER utilizes the concept of passive dynamic locomotion to walk, but when all three feet of the robot are on the ground, the kinematic configuration of the robot behaves like an in-parallel manipulator. To plan and control its change in posture, the kinematics of its forward and inverse displacement must be analyzed. First, the concept of this novel walking robot and its unique tripedal gait are discussed, followed by the overall kinematic configuration and definitions of its coordinate frames. When all three feet of the robot are on the ground, by assuming there is no slipping at the feet, each foot contact point is treated as a passive spherical joint. Kinematic analysis methods for in-parallel manipulators are briefly reviewed and adopted for the forward and inverse displacement analysis for this mobile robot. Both loop-closure equations based on geometric constraints and the intersection of the loci of the feet are utilized to solve the forward displacement problem. Analytical solutions are identified and discussed in the cases of redundant sensing with displacement information from nine, eight, and seven joint angle sensors. For the nonredundant sensing case using information from six joint angle sensors, it is shown that analytical solutions can only be obtained when the displacement information is available from unequally distributed joint angle sensors among the three legs. As for the case when joint angle sensors are equally distributed among the three legs, it will result in a 16th-order polynomial with respect to a single variable, and closed-form forward displacement solutions can be obtained. Finally, results from the simulations are presented for both inverse displacement analysis and the nonredundant sensing case with equally distributed joint angle sensors. It is found that at most 16 forward displacement solutions exist if displacement information from two joint angle sensors per leg are used and one is not used.

Local rolling and tilting capability analysis of fully parallel linear actuated platform-type manipulators

Two problems associated with the local rotatability of two types of fully parallel linearly actuated platform manipulators are investigated in this paper. The first problem is to find the physically allowable region that the movable platform can be freely rolled about any given direction at any specified position. The second problem is to evaluate the maximum angle that the movable platform can be tilted about any given position and orientation. The kinematic constraints involved in these problems are the stroke limitation of the linear actuators, the motion constraints of the passive spherical and universal joints, and the interference condition between the supporting limbs. A unified and computationally efficient approach for solving these problems which takes into account all of the kinematic constraints is developed.

Topology optimisation and singularity analysis of a 3-SPS parallel manipulator with a passive constraining spherical joint

This study focuses on topology optimisation and singularity analysis of a 3-SPS parallel manipulator with three identical limbs made of spherical + prismatic + spherical joints, and a passive spherical joint connecting a moving platform to a fixed base. First, the number synthesis for spatial parallel manipulators with three limbs is reviewed and the existence conditions for the parallel manipulator considered in this study are presented. Second, the inverse position formulation is established; a constrained optimisation algorithm based on the condition number of the manipulator Jacobian matrix over the entire workspace of the manipulator is employed to determine design parameters. A set of optimisation trials is accomplished to prove that the algorithm is valid for determining the optimum values of the manipulator design parameters. Third, forward and inverse Jacobian matrices are derived, and then the singularity loci of the manipulator with different values of the design parameters are generated using a methodology not requiring the explicit expressions for the roots of the determinant of the Jacobians. The singularity loci have been presented to show that this methodology is an efficient and versatile technique in the singularity determination of manipulators, and that a well-conditioned workspace has the least number of singular configurations.

Direct kinematic analysis of 3-RS parallel mechanisms

This article presents a direct kinematic analysis of 3-RS parallel mechanisms. A 3-RS parallel mechanism consists of a fixed base and a moving platform connected by three serial chains, with each serial chain containing one passive revolute joint and one passive spherical joint. A variety of 3-RS mechanisms have been proposed in the literature, to overcome the disadvantages of small workspace characteristic of Stewart platforms and other 6–6 parallel mechanisms. We provide a computationally efficient method to solve the direct kinematics problem for general 3-RS mechanisms. By appealing to Sylvester's dialytic elimination method, the direct kinematics problem can be reduced to the solution of a 16th order polynomial equation in a single variable. In our approach the polynomial coefficients are represented in terms of convolutions of vectors, which considerably simplifies the coding of the algorithm, and unlike existing approaches does not rely on symbolic computation software. The method is applied to the direct kinematic analysis of the Eclipse, a novel six d.o.f. 3-RS parallel mechanism designed for five-face machining.