Kinematics and Dynamics Modeling of Spherical Parallel Manipulator

Mahdizadeh, Omid; Meymand, Afshin Zeinaddini; Mollahossein, Mojtaba; Moosavian, S. Ali A.

doi:10.1109/icrom.2018.8657504

Cited by 6 publications

(5 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The detailed expression is given by (11), such as: cos α cos β cos α sin β sin γ sin α cos γ cos α sin β cos γ sin α cos γ sin α cos β sin α sin β sin γ cos α cos γ sin α sin β cos γ cos α sin γ sin β cos β sin γ cos β cos γ…”

Section: Figure 9 Euler Angles Zyx (α β γ)mentioning

confidence: 99%

“…This structure proves its efficiency and is retained as a main used structure for the next published research. Several methods can be cited, such as the geometrical method, the screw theory, and the Euler angles [8][9][10][11][12][13]. Gosselin and Hamel performed a kinematic optimization to determine the dimensional parameters of the prototype that would provide the best overall accuracy [3].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Djennane,

Chehaidia,

Yakoub

et al. 2024

IEEE Access

View full text Add to dashboard Cite

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.

show abstract

Section: Figure 9 Euler Angles Zyx (α β γ)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Djennane,

Chehaidia,

Yakoub

et al. 2024

IEEE Access

View full text Add to dashboard Cite

show abstract

“…In [61] a different geometric approach was shown specifically for the optimal SPM. In addition, related and similar solutions to the aforementioned methods were applied in [16], [27], [67], and [80].…”

Section: ) Inverse Kinematicsmentioning

confidence: 99%

“…A direct algebraic solution was presented in [54]. A geometric formulation yielding results for the individual assembly modes was shown in [61] for the optimal SPM. Basically, the problem solution can also be found by numerically solving a system of nine equations, expressing the constraint conditions of the assembly, as e.g.…”

Section: ) Inverse Kinematicsmentioning

confidence: 99%

“…−1 for the left-branch-config., (61) which expresses the specific mechanical layout of the manipulator. Essentially, directly including the chosen layout into the solution to the inverse kinematics results in a unique solution, as this removes the mathematical possibility for two configurations to exits in comparison to a general algebraic approach for the inverse kinematics.…”

Section: E: Branch Selectionmentioning

confidence: 99%

See 1 more Smart Citation

Kinematics of a Novel Serial-Parallel, Compliant, Three-Legged Robot

Feller

2023

IEEE Access

View full text Add to dashboard Cite

In this article, the solution to the inverse and forward kinematics of a novel three-legged, serialparallel, compliant robot are presented. The design of the robot aims to combine properties from serial and parallel architectures, thereby targeting an agile, yet precisely controllable robot that possibly allows both for dynamic locomotion and accurate manipulation tasks. The robot embodies the series connection of two parallel architectures, a planar and a spherical mechanism, realized in a highly dense mechanical assembly, allowing for lightweight, functionally redundant and compliant 4-DOF legs. A hybrid compliance behaviour is achieved, serving as a threshold between a stiff and compliant systemic state of the robot. Based on the mechanism design, the study involves the derivation of an alternative, yet complete solution for the inverse and forward kinematics of the spherical parallel manipulator (SPM). The approach utilizes spherical trigonometry and spatial vector geometry and yields a unique solution, while being both easy to implement and numerically efficient, thereby being applicable to real time implementations. Conceptually, a reduction of the mechanism assembly and working modes was directly integrated into the solution terms, drastically simplifying the expressions as they only represents the mechanically meaningful configuration relevant for actual physical systems. In addition to the active joint coordinates, the solution yields a unique set of all passively driven joints. The derived robot kinematics are furthermore verified through a 3D simulation model, showing the robot performing several motions. Thereby, the simulations portray the characteristics of the motor units by means of their corresponding phase profiles, revealing a balanced utilisation.INDEX TERMS Forward kinematics, inverse kinematics, legged robot, mechanical design, serial-parallel mechanism, spherical parallel manipulator.

show abstract