Kinematics Analysis of a Class of Spherical PKMs by Projective Angles

Legnani, Giovanni; Fassi, Irene

doi:10.3390/robotics7040059

Cited by 6 publications

(4 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…Alternatively, in [51] a solution based on spherical analytical theory was proposed. Recently, a solution based on projective angles was shown in [59].…”

Section: ) Inverse Kinematicsmentioning

confidence: 99%

“…Since the orientation of axes ûj is equal to the shape of a trirectangular tetrahedron, (59) expresses the relationship between the altitude of the tetrahedron and the lengths of its sides, which is a trigonometric property as stated in [32, p. 41]. In the isotropic pose, the planes spanned by the arcs of the proximal and distal link are oriented orthogonal to each other, which-since it holds l uv,j = l vw,j = π/2-naturally yields that base and tool axes must equally retain a right-angled configuration.…”

Section: D: Construction Of the Optimal Spm Axesmentioning

confidence: 99%

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

“…The use of 3D orientation ensured by the parallel spherical structure of the robot enhances the performance of active vision. In addition, detailed kinematic analysis of agile eye parallel spherical robot is presented in [27]. The design and development of a spherical parallel robot is proposed by [28], ensuring as application domain the laser pointing tasks.…”

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

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

Kinematics Analysis of a Class of Spherical PKMs by Projective Angles

Cited by 6 publications

References 38 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

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

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

Contact Info

Product

Resources

About