On the stiffness analysis of robotic manipulators and calculation of stiffness indices

Raoofian, Ali; Taghvaeipour, Afshin; Kamali, E Ali

doi:10.1016/j.mechmachtheory.2018.08.025

Cited by 31 publications

(24 citation statements)

References 33 publications

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“…where Q i is a 6 × 6 matrix that transforms the attached coordinate frame to the global reference frame [45]. For the sake of simplicity, it is also assumed that the z-axis of the attached coordinate frame is along the joint axis.…”

Section: Modified Joint-based Constraint Wrench Analysismentioning

confidence: 99%

“…In such systems, there are characteristic matrices, such as Jacobian, stiffness, and mass matrices, which correspond to the aforementioned behavior. Based on these characteristic matrices, researchers have tried to define proper performance indices, such as kinematic index [40], dynamic indices [17,41], and stiffness indices [17,41,19,45,[47][48][49]. In the current study, the CTM was also introduced as another pivotal matrix in mechanical systems which transfers the constraint wrenches from the joints to the center of mass of links.…”

Section: Constraints Distribution Indicesmentioning

confidence: 99%

“…21, in contrast to Table I. The specifications of the Delta's components [45]. the link-based method, the joint-based counterparts do not provide the components of constraint force and moment vectors with respect to a specific coordinate frame.…”

Section: Case Study B: the Delta Parallel Robotmentioning

confidence: 99%

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Revisiting screw theory-based approaches in the constraint wrench analysis of robotic systems

Taghvaeipour

2021

Robotica

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This paper aims at shedding lights on two approaches that were recently proposed for the constraint wrench analysis of robotic manipulators. Both approaches benefit from the Newton–Euler equations, screw notations, and constraint transformation matrices (CTM) to cope with the inverse dynamic problem of multibody systems. In the first approach, which is called the joint-based method, the constraint transformation matrices are derived directly from the kinematic constraints which are imposed on the rigid links by kinematic pairs. In the second approach, which is referred to as the link-based method; however, the constraint matrices are obtained based on the wrench transfer formula of each rigid link. In this study, by resorting to the definition of reciprocal screws, the former methodology is further enhanced to a new version as well. Moreover, based on the proposed modified joint-based CTM, constraint forces and moments distribution indices are introduced. The three constraint wrench analysis methodologies, two joint-based and one link-based, result in different CTMs and set of equations as well, which will be discussed in detail. In the end, on two case studies, a spherical four-bar linkage and a Delta parallel robot, the pros and cons of all three constraint wrench analysis methodologies are discussed, and the proposed indices will be examined. The numerical results reveal that, although all three methods identically compute the magnitude of the applied and constraint force and moment vectors, the joint-based approaches do not report the constraint components with respect to a specific coordinate frame. Moreover, it is shown that the proposed indices can approximately predict the constraint forces and moments distribution at joints, which can be used as force transmission indicators in multibody systems.

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Section: Modified Joint-based Constraint Wrench Analysismentioning

confidence: 99%

Section: Constraints Distribution Indicesmentioning

confidence: 99%

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Revisiting screw theory-based approaches in the constraint wrench analysis of robotic systems

Taghvaeipour

2021

Robotica

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“…7 Hence, the Cartesian space stiffness matrices of complex parallel manipulators are simply obtained following general steps by MSA. 7–10 However, MSA has a disadvantage that it has a heavy calculation burden of the inversion of a matrix with high dimension. Klimchik compared calculation complexity of several methods measured by the number of floating-point operations, and concluded that the calculation complexity of the MSA was on the order of 10 7 –10 8 in the analysis of three types of parallel manipulators while that of the VJM was only on the order of 10 3 with comparable precision.…”

Section: Introductionmentioning

confidence: 99%

A virtual joint method of analytical form for parallel manipulators

Zhang

Han

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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Oriented towards the stiffness optimization of parallel manipulators, a stiffness modeling method based on subspace analysis was proposed. The paper revealed the “shielding effect” of passive joints, i.e. shielding the partial local stiffness of a mechanism on Cartesian space, and accordingly brought forward the concept of Effective Stiffness Tensor (EST), which was then obtained by introducing the orthogonal projector. The method allows a stiffness model of analytical form as well as high computation efficiency, which makes it suitable for applications in the stiffness optimization of parallel manipulators. Proposed method had been applied to the parallel alignment mechanism in China’s large space telescope and verified by dynamic experiments.

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“…One is commonly used in industrial robots that consider the absolute end-effector deflection. In this approach, a specific position or a trajectory is given to the robot, and its positioning error is observed under external wrenches [8,12,13]. The procedures of this kind of evaluation are given in ANSI and ISO standards [4,14].…”

Section: Introductionmentioning

confidence: 99%