Workspace of parallel kinematics machines with minimum stiffness limits: Collinear stiffness value based approach

Portman, Vladimir T.; Chapsky, Vladimir; Shneor, Y.

doi:10.1016/j.mechmachtheory.2011.11.002

Cited by 29 publications

(9 citation statements)

References 14 publications

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“…The stiffness of the contacting surface is considered for the first time in establishing the dynamic equations of Free-Hex machine. Then the dynamic characteristics affected by the attachment stiffness, as well as the masses, damping and stiffness of the legs [22,23,24], can be analyzed separately to explore the performance variation at arbitrary machine configurations, which can help to forecast the machine performance and guarantee the quality in the preparation stage [25].…”

Section: Dynamic Modelling Of Free-hex Machine Toolmentioning

confidence: 99%

Parametric vibration analysis and validation for a novel portable hexapod machine tool attached to surfaces with unequal stiffness

Dong

Palmer

et al. 2019

Journal of Manufacturing Processes

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The Free-Leg Hexapod (Free-Hex) machine tool is an advancement from the conventional Stewart platform, which has the fixed base platform removed to enable the limbs to be attached to a wider range of surfaces (e.g. non-flat and curved). However, in some scenarios (e.g. in-situ repair of industrial installations), the limbs of the Free-Hex need to be attached to the surfaces with unequal stiffness, which brings the challenge of predicting the dynamics of the system for conducting machining operations under dynamically stable conditions. In this paper, after introducing the attachment stiffness (i.e. feet attached to the environment with different materials) in the conventional dynamic model of the parallel manipulator, the dynamic behavior of the Free-Hex machine tools devoted to the insitu operation environments was studied. Then, the experimental validation was conducted to prove the dynamic model developed in this paper. It was found that the errors of the proposed model are under 6% (i.e. 5.1% at symmetrical limb configuration and 5.8% at the arbitrary configuration) when the limbs are attached to the surfaces with unequal stiffness. Further, by applying the validated model, the dynamic performance of the Free-Hex with a wider range of attachment stiffness was analyzed. Overall, it was found that the attachment stiffness has a remarkable influence on the natural frequencies of the machine tool (e.g. the frequency of mode 4 at the symmetrical configuration is increased by 36.8% when the attachment stiffness of one limb changes from 0 to 1e+12 N/m). Thus, the work discussed in this paper can be utilized to avoid the dynamically unstable configurations of parallel kinematic machine tools (e.g. Free-Hex) when mounting on the surface with unequal stiffness in the in-situ operation environments.

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Section: Dynamic Modelling Of Free-hex Machine Toolmentioning

confidence: 99%

Parametric vibration analysis and validation for a novel portable hexapod machine tool attached to surfaces with unequal stiffness

Dong

Palmer

et al. 2019

Journal of Manufacturing Processes

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“…Other related stiffness modeling and kinematic analyses of different parallel manipulators can also be found. [25][26][27][28][29][30][31][32][33][34][35][36] In this paper, the stiffness model of the Tri-pyramid Robot will be established based on the overall Jacobian matrix method. Li and Xu 37,38 analyzed stiffness models of two 3-DOF TPMs based on the overall Jacobian matrix method, while Wang et al 39 presented a more detailed analytical approach for the stiffness modeling of the Tricept Robot by using the overall Jacobian matrix.…”

Section: Nomenclaturementioning

confidence: 99%

Tri-pyramid Robot: stiffness modeling of a 3-DOF translational parallel manipulator

Zeng¹,

Ehmann

Cao

2014

Robotica

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SUMMARYThis paper presents a 3-DOF (degree of freedom) translational parallel manipulator named the Tri-pyramid Robot. Compared to the developed 3-DOF translational parallel manipulators, the Tri-pyramid Robot is designed based on conical displacement subset to exhibit better kinematic characteristic. The inverse position solution is obtained through closed-loop constraint analysis and used to formulate the overall Jacobian matrix of constraints and actuations based on the theory of reciprocal screws. Furthermore, by considering the stiffness of all links, joints, actuators, fixed, and moving platforms, the output stiffness matrix of the Tri-pyramid Robot is derived by the transformations of loads and deformations in the closed-loop form. The relations between the virtual input-output displacements are analyzed by the overall Jacobian matrix and used to build the manipulator's stiffness model. Stiffness performance is evaluated by the extreme eigenvalues of the output stiffness matrix in the reachable workspace. By considering the variations of the structural parameters and the distribution of the output stiffness, the maximal stiffness workspace is obtained through numerical optimization, providing, thereby, basic constraints for the parametric design of the Tri-pyramid Robot.

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“…The stiffness of parallel manipulator is closely related to its accuracy, which means that it is very important to study the stiffness. Portman et al 14 studied the parallel machine tool using the minimum stiffness index in the workspace. Wang et al 15 used the full rank of Jacobian matrix and analysed the stiffness of a Tricept parallel manipulator.…”

Section: Introductionmentioning

confidence: 99%

Performance analysis for a 2 (3HSS+S) parallel manipulator with double moving platforms

Zhao

Shan

2016

International Journal of Advanced Robotic Systems

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The working efficiency of a parallel manipulator with double moving platforms is better than a parallel manipulator with a single moving platform. In this study, a 2 (3HSSþS) parallel manipulator is presented, and the topology model of the parallel manipulator is established. After calculating, the position and velocity of the manipulator were analysed, and the workspace was obtained under the constraint conditions of parallel manipulator. Within the workspace, the motion dexterity was studied using the reciprocal of the condition number of the motion Jacobian matrix. The static load-bearing performance was analysed through the two norms of the force Jacobian matrix. The two performance indices, which are motion dexterity and static load bearing, indicate that the manipulator has favourable performance characteristics in the range of positive values of angle, which is the rotation in z-axis, but it has a singular position in the range of large negative values of angle. Within the scope of the singular point, the maximum and minimum eigenvalues of the stiffness matrix and the kinematic stiffness index (KSI) were analysed. It has been concluded that the stiffness characteristics are poor near the singular points, and the correctness analysis of the two performance indices has been verified by the results.

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Workspace of parallel kinematics machines with minimum stiffness limits: Collinear stiffness value based approach

Cited by 29 publications

References 14 publications

Parametric vibration analysis and validation for a novel portable hexapod machine tool attached to surfaces with unequal stiffness

Parametric vibration analysis and validation for a novel portable hexapod machine tool attached to surfaces with unequal stiffness

Tri-pyramid Robot: stiffness modeling of a 3-DOF translational parallel manipulator

Performance analysis for a 2 (3HSS+S) parallel manipulator with double moving platforms

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