Forward Kinematics of a General Fully Parallel Manipulator with Auxiliary Sensors

Chiu, Yu-Jen; Perng, Ming-Hwei

doi:10.1177/02783640122067462

Cited by 38 publications

(24 citation statements)

References 15 publications

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“…In contrast, the second approach consists of adding extra sensors for obtaining additional information about the parallel mechanism's state [21][22][23][24][25][26][27][28]. These can be, for example, angular sensors that are placed on the base or the manipulator platform joints or linear and/or angular sensors that are placed on supplementary passive legs.…”

Section: Introductionmentioning

confidence: 99%

On the Direct Kinematics Problem of Parallel Mechanisms

Seibel

Schulz

Schlattmann

2018

Journal of Robotics

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The direct kinematics problem of parallel mechanisms, that is, determining the pose of the manipulator platform from the linear actuators' lengths, is, in general, uniquely not solvable. For this reason, instead of measuring the lengths of the linear actuators, we propose measuring their orientations and, in most cases, also the orientation of the manipulator platform. This allows the design of a low-cost sensor system for parallel mechanisms that completely renounces length measurements and provides a unique solution of their direct kinematics.

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Section: Introductionmentioning

confidence: 99%

On the Direct Kinematics Problem of Parallel Mechanisms

Seibel

Schulz

Schlattmann

2018

Journal of Robotics

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“…However, the type, number and location of the redundant sensors must be chosen very carefully to define a unique solution. Otherwise, it can cause additional problems such as workspace limitations due to the passive legs or joint arrangements, as mentioned in Reference [53]. Furthermore, different sensor types can even reduce the quality of the output by introducing time delays and unwarranted confidences.…”

Section: Additional Sensor Solutionmentioning

confidence: 99%

Performance Evaluation of a Sensor Concept for Solving the Direct Kinematics Problem of General Planar 3-RPR Parallel Mechanisms by Using Solely the Linear Actuators’ Orientations

Schulz

2019

Robotics

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In this paper, we experimentally evaluate the performance of a sensor concept for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism by using solely the linear actuators’ orientations. At first, we review classical methods for solving the direct kinematics problem of parallel mechanisms and discuss their disadvantages on the example of the general planar 3-RPR parallel mechanism, a planar parallel robot with two translational and one rotational degrees of freedom, where P denotes active prismatic joints and R denotes passive revolute joints. In order to avoid these disadvantages, we present a sensor concept together with an analytical formulation for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism where the number of possible assembly modes can be significantly reduced when the linear actuators’ orientations are used instead of their lengths. By measuring the orientations of the linear actuators, provided, for example, by inertial measurement units, only two assembly modes exist. Finally, we investigate the accuracy of our direct kinematics solution under static as well as dynamic conditions by performing experiments on a specially designed prototype. We also investigate the solution formulation’s amplification of measurement noise on the calculated pose and show that the Cramér-Rao lower bound can be used to estimate the lower bound of the expected variances for a specific pose based exclusively on the variances of the linear actuators’ orientations.

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“…Naturally, an elementary condition to apply equation (24) is that the Jacobian matrix J i must be invertible; otherwise the ith limb is at a singular configuration.…”

Section: Velocity Analysismentioning

confidence: 99%

Kinematics of a hyper-redundant manipulator by means of screw theory

Gallardo-Alvarado

Rico-Martínez

2009

Proceedings of the Institution of Mechanical Engineers, Part K:

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In this work the kinematics of a hyper-redundant manipulator built with an optional number of parallel manipulators with identical topologies assembled in series connection is carried out by using the theory of screws. First, closed-form solutions to solve the kinematics, up to the acceleration analysis, of the base module, an asymmetrical three-degree-of-freedom (dof ) parallel manipulator with mixed motions, are derived using geometric procedures and the theory of screws; later, the symbolic results thus obtained are applied recursively to solve the kinematics of the proposed hyper-redundant manipulator. A 12-dof hyper-redundant manipulator is included as a case study.are among the most important benefits of such an exceptional degree of manipulability. Examples of the excellent performance of HRMs can be found in nature itself, giving rise to several complex mechanisms with adopted names such as snake [2], serpentine [3], tentacle [4], or elephant's trunk [5]. On the other hand, HRMs are considered as not anthropomorphic, and because of the lack of an effective methodology of kinematic analysis, both finite and infinitesimal, in addition to programming problems, HRMs remained only as laboratory curiosities a few years ago.Since the pioneering contribution of Anderson and Horn [6], traditionally HRMs are obtained by assembling in series connection several parallel manipulators with identical limbs, called symmetrical parallel manipulators, see for instance references [7] to [13]. Certainly, the merits of SPMs such as simplified mechanical assembly and minimum cost (because of identical mechanical components and repetitive manufacturing operations) are factors to be considered in the design process of an HRM. However, another type of mechanical architecture known as asymmetrical parallel manipulators are emerging requesting an opportunity to play a central role in the development of HRMs. The easy generation of closed-form solutions, which is prohibitive for most SPMs, for solving the finite kinematics is the main attraction of APMs. JMBD188

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Forward Kinematics of a General Fully Parallel Manipulator with Auxiliary Sensors

Cited by 38 publications

References 15 publications

On the Direct Kinematics Problem of Parallel Mechanisms

On the Direct Kinematics Problem of Parallel Mechanisms

Performance Evaluation of a Sensor Concept for Solving the Direct Kinematics Problem of General Planar 3-RPR Parallel Mechanisms by Using Solely the Linear Actuators’ Orientations

Kinematics of a hyper-redundant manipulator by means of screw theory

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