Computation of Unique Kinematic Solutions of a Spherical Parallel Manipulator with Coaxial Input Shafts

Tursynbek, Iliyas; Niyetkaliye, Aibek; Shintemirov, Almas

doi:10.1109/coase.2019.8843090

Cited by 14 publications

(10 citation statements)

References 41 publications

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“…So far, most studies have focused on the kinematic issues of RSPMs, while quite a few have referred to the dynamic control of these robots. For RSPMs, several studies have been reported on a variety of relevant problems, which include modeling of workspace in joint and Cartesian space [14][15][16][17], inverse and forward kinematic analysis to obtain analytically unique real-time solutions [18][19][20][21][22][23][24][25], design and optimization [26][27][28][29][30][31][32], design and robustness [33], singularity analysis, and derivation of Jacobian matrices [34,35]. However, the constrained kinematic analysis has gone unnoticed in the literature.…”

Section: Mathematical Modeling Challenges and Control Strategiesmentioning

confidence: 99%

Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

Ahmadi N,

Kamali Eigoli,

Taghvaeipour

2024

Robotica

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This research offers an adaptive model-based methodology for autonomous control of 3-RRR spherical parallel manipulator (RSPM) based on a novel modeling framework. RSPM is an overconstrained parallel mechanism that has a variety of applications in medical procedures such as ankle rehabilitation because of its precision and accuracy. However, obtaining a complete explicit dynamic model of these mechanisms for tracking purposes has been a problematic challenge due to their inherent singularities, coupling effects of the limbs, and redundant constraints imposed by the intermediate joints. This paper presents a novel algorithm to obtain the analytical kinematic solutions of RSPMs based on the closed-loop vector method, which includes constraint analysis. By incorporating constrained kinematics into the dynamic model, a comprehensive explicit dynamic solution of the non-overconstrained version 3-RCC of RSPM is developed in task space, based on screw theory and the linear homogeneous property of algebraic equations on the manipulator twist. Based on the proposed computational framework, a robust self-tuning backstepping control (STBC) strategy is applied to the robot to overcome the effect of external disturbances and time-varying uncertainties. Furthermore, an observer-based compensation (OBC) method is presented for dealing with the nonlinear hysteresis loops of the ankle during trajectory tracking purposes. The closed-loop stability of the whole system including STBC and OBC is theoretically performed by Lyapunov methods. The proposed methodologies are validated by realistic co-simulations in different scenarios. For instant, in the presence of external disturbances, the maximum tracking error norm of STBC is 37.5% less than the sliding mode approach.

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Section: Mathematical Modeling Challenges and Control Strategiesmentioning

confidence: 99%

Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

Ahmadi N,

Kamali Eigoli,

Taghvaeipour

2024

Robotica

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“…The robot is designed to operate within a significantly larger working space than the human eye while maintaining high precision and dynamic performance. Numerous research studies have been conducted on the agile eye, resulting in the emergence of various parallel manipulator models, such as the simple SPM, compact SPM, simplified SPM a 2 DOF, and coaxial SPM [3][4][5][6]. Errors are introduced into the kinematics of parallel robots as a result of manufacturing procedures.…”

Section: Introductionmentioning

confidence: 99%

Design, Analysis, and Implementation of a 3-DOF Spherical Parallel Manipulator

Djennane,

Chehaidia,

Yakoub

et al. 2024

IEEE Access

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The agile eye is classified as a 3-degrees of freedom (DOF) type 3-RRR spherical parallel mechanism (SPM) designed to replicate the movement patterns seen in the human eye. The end organ exhibits a range of motion inside a cone of vision spanning 140°, with a twist tolerance of ±30°.Additionally, the mechanism can achieve angular velocities exceeding 1000 °/s and angular accelerations surpassing 20 °/s 2 . The objective of this research is to conduct a comprehensive examination of the direct and inverse kinematics of the spatial parallel manipulator (SPM) on a manipulator. The purpose of doing a kinematic analysis on the manipulator is to enhance the design optimization process, accurately determine the dimensions of all components, and improve the functionality of the computer-aided design (CAD) system. This study aims to ensure the efficient operation of the SPM and maximize its available workspace. Additionally, this study enables the achievement of a high level of stiffness inside the workspace and the establishment of clearly comprehensible limits for the workspace. Moreover, it facilitates the precise control of the SPM. An evaluation is conducted to assess the efficacy of the existing technique by comparing its outputs with those obtained from a virtual reality simulation using the commercially available software CopeliaSim. The control mechanism described in the present paper demonstrates a surplus in the resolution of precision problems while ensuring competitiveness at a controlled cost. The implementation of the robot revealed the effectiveness of the design approach adopted by recording an error of no more than 1%. INDEX TERMSMechatronics; Precision engineering; Spherical parallel manipulator; Euler angles; Optimization; Implementation. NOMENCLATURE Ui Unit vectors directed along the axes of the actuators Ai K Dexterity γ Angle between the actuators axes Ai. ‖.‖ Euclidean norm of the matrix Vi Unit vectors directed along the axes of the pivot joints connected to the end effectors Bi. ζ Reciprocal number Wi Unit vectors directed along the axes of the intermediate pivot joints Ci. η Global index for the optimization of robot α1 Angle between Ai and Ci. W Working space of the α2 Angle between Ci and Bi. kappamin Minimum dexterity β Angle between the normal of the base and the actuators axes Ai. Vi Initial state vector of the manipulator θ Angle of rotation motor. R Rotation matrix J Jacobean matrices of the manipulator W1, W2, W3 Projections of Wi vectors in the fixed frame This article has been accepted for publication in IEEE Access.

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“…YEN JUNG CHEN, WEI-CHENG TUNG, WEI-RUI LEE, BRIJESH PATEL, VYTAUTAS BUČINSKAS, MODRIS GREITANS, PO TING LIN 2 ROBOTIC SYSTEMS AND APPLICATIONS [8], SPM can be considered when designing robotic wrists [9] due to their manipulator characteristics and high load-carrying capability. SPM provides different applications, which include medical tools [10,11], moving platforms [12], advanced robotic systems [13], Tactile devices [14], and rehabilitation [15]. SPM was classified into four major groups based on the Lie group of displacements using the synthesis approach [16].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, a 3D-printed spherical mechanism [12] was used for testing and control. The mechanism is driven by the servos using a combination of three pinions and internal gears, each of them connected to one of the arms of the platform and capable of steering them in a constrained circular path; this also maintains the platform's center at the same location regardless of how it rotates or tilts.…”

Section: Introductionmentioning

confidence: 99%

“…a) 3D software model design b) 3D printed spherical platform mechanism[12] Spherical platform mechanism with three parallel motors However, the system appears frail and unstable due to the design placing three isolated gears without further support. Then the modification in design was done by implementing three internal gears with the exchange of three gears in the middle as they rotate along the same axis.…”

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confidence: 99%

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Designing and controlling a self-balancing platform mechanism based on 3-RCC spherical parallel manipulator

Chen¹,

Tung²,

Lee³

et al. 2023

Robot. syst., appl.

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Motion control platforms have various applications in the manufacturing and automation industries. Different literature provides multiple issues related to the kinematics and dynamics of self-guided robots for transportation regarding platform balancing. Self-balancing platforms are utilized in many deliveries, stabilization, and transportation systems, and they are especially well suited for outdoor activities when the ground surface is not flat or structured. This paper describes developing a control technique for a self-balancing platform using the 3-RCC spherical parallel manipulator. This mechanism was designed to support an AGV (Automated Guided Vehicle) for transporting and lifting heavy weights for industrial applications. The AGV carries a robotic arm on top for different tasks. When the AGV encounters a steep slope or a rough surface, the AGV tilts, and the robotic arm’s performance is significantly affected. So, this study gives a solution to avoid these circumstances with a novel approach for the platform’s self-balancing mechanism consisting of a 3-RCC spherical parallel manipulator. Real-time stabilization and kinematics analysis methods are used to achieve the self-balancing system of the platform. When both methods are observed through different tilting angles for automation stability, Kinematic analysis performs more efficiently with less time duration when compared with the real-time stabilization method.

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Computation of Unique Kinematic Solutions of a Spherical Parallel Manipulator with Coaxial Input Shafts

Cited by 14 publications

References 41 publications

Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

Design, Analysis, and Implementation of a 3-DOF Spherical Parallel Manipulator

Designing and controlling a self-balancing platform mechanism based on 3-RCC spherical parallel manipulator

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