A Simple Method to Solve the Instantaneous Kinematics of the 5-RUR Parallel Manipulator

Gallardo-Alvarado, Jaime; Abedinnasab, Mohammad H.; Islam, Md. Nazrul

doi:10.1017/s0263574718001509

Cited by 7 publications

(5 citation statements)

References 31 publications

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“…The translational component of the operational space coordinates x t = (0) r D is the vector to the desired end effector frame relative to the base frame. The rotational component marks the pointing direction of the end effector frame with the two angles x r =[ϕ x , ϕ y ], as established in literature [16,14,1,18,7] with ϕ z =0. To allow general (tool) frame definitions, using X-Y -Z Tait-Bryan angles for the full orientation of the end effector frame gives the SO (3)…”

Section: Inverse Kinematic Model For 3t2r Parallel Robotsmentioning

confidence: 99%

“…Symmetric 3T2R PMs with identical limbs were shown to exist rather late [5,9]. Since then, works on analysis, modeling and synthesis of these types of PMs have increased [16,7].…”

Section: Introduction and State Of The Artmentioning

confidence: 99%

“…The analysis of symmetric 3T2R PMs can be performed by several methods. Most prominent is screw theory [5,10,13,7], which can be extended by other algebraic and geometric concepts like Grassmann-Cayley algebra and Grassmann geometry [1] or algebraic geometry (Study parameters and Gröbner bases) [13]. For the related 2T3R PMs Lie groups of displacements were used in [11].…”

Section: Introduction and State Of The Artmentioning

confidence: 99%

See 2 more Smart Citations

Structural and Dimensional Synthesis of Overconstraint Symmetric 3T2R Parallel Robots Using Tait-Bryan-Angle Kinematic Constraints

Schappler

2022

Springer Proceedings in Advanced Robotics

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The basic parallel robotics principle of defining kinematic constraints as vector loops is transferred from the general 3T3R case to the 3T2R case by applying a nonlinear Tait-Bryan-angle rotation constraint using the intrinsic Z-Y -X convention. This presents an alternative way to the deduction of differential inverse kinematics by the theory of linear transformations. The resulting formulation is used in a permutational combined structural and dimensional synthesis. The modular approach allows to combine databases of serial and parallel robots without manual intervention. The validation shows the reproducibility of existing kinematic structures using the new kinematic formulation. The optimization scheme allows to obtain suitably dimensioned symmetric 3T2R parallel robots for a given task.

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Section: Inverse Kinematic Model For 3t2r Parallel Robotsmentioning

confidence: 99%

“…Symmetric 3T2R PMs with identical limbs were shown to exist rather late [5,9]. Since then, works on analysis, modeling and synthesis of these types of PMs have increased [16,7].…”

Section: Introduction and State Of The Artmentioning

confidence: 99%

Section: Introduction and State Of The Artmentioning

confidence: 99%

See 1 more Smart Citation

Structural and Dimensional Synthesis of Overconstraint Symmetric 3T2R Parallel Robots Using Tait-Bryan-Angle Kinematic Constraints

Schappler

2022

Springer Proceedings in Advanced Robotics

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“…Bu [26] developed a novel metric based on the geometric average normalized volume spanned by weighted screws to measure the distance from the current configuration to a singular configuration. Gallardo [27] obtained the input-output equations of velocity and acceleration of the 5-RPUR parallel mechanism by resorting to reciprocal screws.…”

Section: Introductionmentioning

confidence: 99%

Distribution Characteristics of Screw Axes Belonging to General Three-System of Screws

2022

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The cylindroid describes the exact distribution of the ∞1 screw axes of the general two−system of screws. For the general three−system, this article introduces the surface on which lies the position vector endpoints of its ∞2 screw axes, and then develops the finite distribution zone in which they most densely distribute. In particular, this paper explores the inner structure of the zone by partitioning the general three−system into ∞1 two−subsystems, and then reveals the principle of constructing the distribution space of the general three−system by that of the general two−system in Euclidean three−space. In pursuit of a generalized decomposition method, we propose the varying−pitch ruled surface carrying the screws whose pitch value continuously varies according to any desired function rule, based on the pitch−hyperboloid carrying all the equal−pitch screws. This investigation provides some useful guides for the axode planning and then the motion planning of three degree−of−freedom parallel mechanisms.

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“…Due to the complex topological structure of multiclosed-loop robotic manipulators or parallel robots, the dynamic modeling problem of these robotic mechanical systems has received increasing attention over the past decades [1,2,[9][10][11][12]. However, most existing dynamic models on the complex multi-closed-loop mechanism mainly aim to achieve its optimal design and performance analysis [11][12][13][14]. With respect to the real-time control of multi-closed-loop robotic manipulators, an ideal dynamic model should be simple, highly computational efficient, and accurate enough to represent the physical system.…”

Section: Introductionmentioning

confidence: 99%

Reduced Dynamic Modeling for Heavy-Duty Hydraulic Manipulators With Multi-Closed-Loop Mechanisms

2020

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A reduced dynamic modeling approach is introduced to systematically establish explicit closed-form dynamic equations for the main motion system of a heavy-duty hydraulic manipulator with multi-closed-loop mechanisms. The harmonious combination of the reduced system dynamic method with Lagrangian formulation, the principle of virtual work and screw theory greatly reduces the tedious calculation and largely simplifies the derivation of explicit control-orientated closed-form dynamic equations for complex multi-closed-loop mechanisms. Only three coupled subsystems, two Jacobian matrices, and two Hessian matrices are involved, thereby greatly reducing the order and the complexity of the closed-form dynamic equations. In addition to calculating the two Jacobian matrices by screw theory, the two Hessian matrices are also calculated straightforwardly by screw theory, thereby avoiding the difficulty in obtaining Hessian matrices by differentiating the Jacobian matrices and simplifying the calculation of the two Hessian matrices. No parts of dynamic equations are neglected in the derivation of the dynamic model. Thus, the accurate dynamic motion equations for the main motion system are obtained concisely. The derived closed-form dynamic equations are explicit with respect to the system inputs, which facilitate dynamics analysis and controller design. The experiments on the main motion system of the heavy-duty hydraulic forging manipulator demonstrate the efficiency of the proposed approach.

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A Simple Method to Solve the Instantaneous Kinematics of the 5-RUR Parallel Manipulator

Cited by 7 publications

References 31 publications

Structural and Dimensional Synthesis of Overconstraint Symmetric 3T2R Parallel Robots Using Tait-Bryan-Angle Kinematic Constraints

Structural and Dimensional Synthesis of Overconstraint Symmetric 3T2R Parallel Robots Using Tait-Bryan-Angle Kinematic Constraints

Distribution Characteristics of Screw Axes Belonging to General Three-System of Screws

Reduced Dynamic Modeling for Heavy-Duty Hydraulic Manipulators With Multi-Closed-Loop Mechanisms

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