On the Direct Kinematics Problem of Parallel Mechanisms

Seibel, Arthur; Schulz, Stefan; Schlattmann, Josef

doi:10.1155/2018/2412608

Cited by 7 publications

(7 citation statements)

References 32 publications

(47 reference statements)

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“…He concluded that the IMU's accelerometer values might be used for static pose calculations but the achievable accuracy is questionable, especially under dynamic conditions. In previous papers [63][64][65][66] and supported by this paper's results, we came to the same conclusion. However, when using the IMU's gyroscope in addition to the accelerometer, significantly more accurate results can be obtained.…”

Section: Discussionsupporting

confidence: 89%

“…In previous works [63][64][65][66], we presented different formulations to derive the manipulator platform's pose from the linear actuators' orientations and the orientation of the manipulator platform. In this paper, we investigate the applicability for solving the direct kinematics problem under dynamic conditions of a method, in the following referred to as linear least-squares formulation, that uses two of the linear actuators' orientations and the orientation of the manipulator platform and provides a unique solution with each measurement, see, for example, [65].…”

Section: Robust Pose Calculationsmentioning

confidence: 99%

“…Therefore, we encouraged a paradigm shift by avoiding length measurements of the linear actuators at all and using more suitable coordinates for solving the direct kinematics problem [63]. In this context, in previous works [63][64][65][66], we solely used IMUs to measure the linear actuators' orientations and the orientation of the manipulator platform for unambiguously solving the direct kinematics problem of parallel mechanisms. By using inverse kinematics, the linear actuators' lengths can be calculated from the manipulator platform's pose afterwards.…”

Section: Introductionmentioning

confidence: 99%

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On Using Inertial Measurement Units for Solving the Direct Kinematics Problem of Parallel Mechanisms

Schulz

2019

Robotics

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In this paper, we investigate the accuracy and the computational efficiency of an IMU-based approach for solving the direct kinematics problem of parallel mechanisms with length-variable linear actuators under dynamic conditions. By avoiding to measure the linear actuators’ lengths and by using orientations instead, a comprehensive, low-cost sensor structure can be obtained that provides a unique solution for the direct kinematics problem. As a representative example, we apply our approach to the planar 3-RPR parallel mechanism, where P denotes active prismatic joints and R denotes passive revolute joints, and investigate the achievable accuracy and robustness on a specially designed experimental device. In this context, we also investigate the effect of sensor fusion on the achievable accuracy and compare our results with those obtained from linear actuators’ lengths when the Newton-Raphson algorithm is used to compute the manipulator platform’s pose iteratively. Finally, we discuss the applicability of inertial measurement units (IMUs) for solving the direct kinematics problem of parallel mechanisms.

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Section: Discussionsupporting

confidence: 89%

Section: Robust Pose Calculationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Using Inertial Measurement Units for Solving the Direct Kinematics Problem of Parallel Mechanisms

Schulz

2019

Robotics

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“…In order to avoid using the linear actuators' lengths for solving the direct kinematics, we proposed a new sensor concept where the manipulator platform's pose can be uniquely determined from the orientations provided by three inertial measurement units (IMUs) that were placed on top of the manipulator platform as well as on two of the linear actuators [24][25][26]. For measuring the manipulator platform's orientation, additional wiring effort is required that can cause workspace reductions due to the risk of link-wire interferences.…”

Section: Introductionmentioning

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

Self Cite

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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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“…An industrial robot's characteristics of high load capacity, high-precision P&O control, and good stability mean it can offer stable and accurate positioning of heavy components. In recent years, parallel robots have been widely used for P&O of the large components and assemblies, due to these advantages as well as high stiffness and rapid motion [5,6]. Stewart parallel robots (SPRs) are the most frequently used type of parallel robot structure.…”

Section: Introductionmentioning

confidence: 99%

An Alignment Method of Human-Robot Collaboration Based on the Six-Dimensional Force/Torque Dynamic Measurement for Large-Scale Components

Wen

Zhang

et al. 2018

Journal of Robotics

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A Stewart parallel robot (SPR) is a promising choice for alignment or assembly of components that are large or heavy. This paper presents a method for human-robot collaboration, for positioning and orientation of large components. Use of interactive force measurements is important for human-robot collaboration. It is based on six-dimensional force/torque (F/T) measurements. First, the six-dimensional F/T data are calculated based on the six-actuator SPR geometry and screw theory. Second, the effects of gravity forces (dynamic gravity compensation) are considered, and a method to offset their effects is explained. Third, force estimation experiments were performed using an S-type force sensor and known applied test forces. Finally, the F/T-driven feedback was tested for the alignment of a large-scale component. The experimental results show that the calculated six-dimensional F/T can accurately track the force applied to a large and/or heavy component by a human worker. It can also accurately predict the F/T required to compensate for inertial forces and components’ weight. Thus, the alignment method of human-robot collaboration based on the six-dimensional force/torque dynamic measurements for large-scale components is correct and effective.

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On the Direct Kinematics Problem of Parallel Mechanisms

Cited by 7 publications

References 32 publications

On Using Inertial Measurement Units for Solving the Direct Kinematics Problem of Parallel Mechanisms

On Using Inertial Measurement Units for Solving 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

An Alignment Method of Human-Robot Collaboration Based on the Six-Dimensional Force/Torque Dynamic Measurement for Large-Scale Components

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