On the dynamics of parallel manipulators

Yiu, Y.K.; Cheng, Hui; Xiong, Zhenhua; Liu, G.F.; Li, Z.X.

doi:10.1109/robot.2001.933204

Cited by 58 publications

(27 citation statements)

References 9 publications

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“…The Lagrange-D'Alembert Method (Nakamura, 1991, Nakamura & Ghodoussi, 1989, Park et al, 1999, Yiu et al, 2001) makes it possible to systematically convert between the single models of serial kinematic chains to the model of the compact parallel manipulator. In this method, however, it was not shown how the Jacobian matrices of the serial kinematic chains of the tree structure J i can be transformed into the Jacobian of the parallel manipulator G. An algorithm was developed because of that, in order to perform this transformation.…”

Section: New Methods For Derivation Of the Jacobian Matrix Of The Paramentioning

confidence: 99%

“…The Lagrange-D'Alembert formulation represents an elegant and effective consideration of the problem of manipulator's dynamics (Nakamura, 1991, Nakamura & Ghodoussi, 1989, Park et al, 1999, Yiu et al, 2001. Here, no additional multipliers are calculated.…”

Section: Inverse Dynamicsmentioning

confidence: 99%

“…Therefore, in order to determine the relationship between the velocities and accelerations of the active and passive joints, a more suitable solution must be derived (Yiu et al, 2001). For this purpose we introduce the closed kinematic loop constraints of the parallel manipulator:…”

Section: Computation Of the Torquesmentioning

confidence: 99%

“…The Lagrangian method is very widely used in the area of parallel manipulators (Beyer, 1928, Kock, 2001). In particular, two procedures from this family are established here: Namely the Lagrangian equations of the first type (Kang & Mills, 2002, Miller & Clavel, 1992, Murray et al, 1994, Tsai, 1999 and the Lagrange-D'Alembert formulation (Nakamura, 1991, Nakamura & Ghodoussi, 1989, Park et al, 1999, Stachera, 2006a, Stachera, 2006b, Yiu et al, 2001. The use of generalized coordinates is employed in these procedures.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Derivation and Calculation of the Dynamics of Elastic Parallel Manipulators

Stachera¹,

Schumacher²

2008

Automation and Robotics

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Section: New Methods For Derivation Of the Jacobian Matrix Of The Paramentioning

confidence: 99%

Section: Inverse Dynamicsmentioning

confidence: 99%

Section: Computation Of the Torquesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Derivation and Calculation of the Dynamics of Elastic Parallel Manipulators

Stachera¹,

Schumacher²

2008

Automation and Robotics

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“…On the other hand, the Lagrangian approach can be applied by using the Lagrange equation with respect to a minimum set of generalized coordinates. Yiu et al (2001) showed that either application of Lagrange Equation or treelike system analysis are equivalent to one another and lead to the same set of equations when applied to a parallel manipulator. Moreover, similar results were obtained by Murray and Lovell (1989) using the D'Alembert's principle and the principle of virtual work.…”

Section: Development Of the Dynamic Modelsmentioning

confidence: 99%

Solving the dynamic equations of a 3-PRS Parallel Manipulator for efficient model-based designs

2016

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Abstract. Introduction of parallel manipulator systems for different applications areas has influenced many researchers to develop techniques for obtaining accurate and computational efficient inverse dynamic models. Some subject areas make use of these models, such as, optimal design, parameter identification, model based control and even actuation redundancy approaches. In this context, by revisiting some of the current computationally-efficient solutions for obtaining the inverse dynamic model of parallel manipulators, this paper compares three different methods for inverse dynamic modelling of a general, lower mobility, 3-PRS parallel manipulator. The first method obtains the inverse dynamic model by describing the manipulator as three open kinematic chains. Then, vector-loop closure constraints are introduced for obtaining the relationship between the dynamics of the open kinematic chains (such as a serial robot) and the closed chains (such as a parallel robot). The second method exploits certain characteristics of parallel manipulators such that the platform and the links are considered as independent subsystems. The proposed third method is similar to the second method but it uses a different Jacobian matrix formulation in order to reduce computational complexity. Analysis of these numerical formulations will provide fundamental software support for efficient model-based designs. In addition, computational cost reduction presented in this paper can also be an effective guideline for optimal design of this type of manipulator and for real-time embedded control.

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Attitude control of planar end‐effector and estimation of contact point using parallel mechanism

Kubo

Ohnishi

2008

Elect Comm in Japan

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Recently, many robots have been utilized in unknown environment , for example, slave robots of teleoperation systems, walking robots and so on. They are called environment-adaptive robots. In most teleoperation systems, slave manipulators are placed in unknown environment. In the case of walking robots, the paddle foot is a planar end-effector and road surface is unknown environment. They recognize shape of road surface and need to walk on rough terrain. Therefore, it is very important for the environment-adaptive robots to contact stably and to recognize unknown environment. In this paper, a compliance controller of attitude of a planar end-effector is proposed to achieve stable contact with unknown environment. The robot utilized in this research has parallel mechanism as a whole as shown in Fig. 1, since the planar end-effector is supported by three arms. Virtual compliance models are inserted at the end of each arm for compliant motion of the end-effector. On the other hand, position control is also achieved for COG (center of gravity) of the end-effector. Moreover, an estimation method of the contact point without sensors is presented. We assume that only face-to-point contact exists between the end-effector and unknown environment. Reaction torque observer is utilized to estimate reaction force from unknown (a) overview (b) end-effector Fig. 1. Parallel-link manipulator environment. And excessive stress is not exerted on the robots and the environment by means of the proposed controller in the estimation. We carried out some experiments by changing force feedback gain K f. Fig. 2 shows comparison of accuracy in the estimation. d is the distance between the environment and the estimation value. Estimation is achieved with a high degree of accuracy if d is small. α means z-direction displacement of COG of the end-effector after the end-effector contacts the environment. If α increased or K f approaches zero, accuracy was improved as shown in Fig. 2. In this case, reaction force from the environment gets larger and ratio of force exerted on each arm can be detected more accurately. In the case of K f = 1.0 and d = 3.0 mm, correct values were estimated in spite of not exerting excessive stress on the environment. In this paper, face-to-point contact was realized by means of a planar end-effector instead of a spheral end-effector. We proposed compliance controller for attitude of a planar end-effector and an estimation method of the contact point. The validity of the proposed method was shown by the numerical and experimental results. Our new approach of contact motion can be widely applied to the robots using parallel mechanism. Fig. 2. Comparison of estimation accuracy-11

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On the dynamics of parallel manipulators

Cited by 58 publications

References 9 publications

Derivation and Calculation of the Dynamics of Elastic Parallel Manipulators

Derivation and Calculation of the Dynamics of Elastic Parallel Manipulators

Solving the dynamic equations of a 3-PRS Parallel Manipulator for efficient model-based designs

Attitude control of planar end‐effector and estimation of contact point using parallel mechanism

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