Geometric Stiffness Analysis of Wire Robots: A Mechanical Approach

Šurdilović, Dragoljub; Radojicic, Jelena; Krüger, Jörg

doi:10.1007/978-3-642-31988-4_24

Cited by 21 publications

(9 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where I 3×3 ∈ R 3×3 and 0 3×3 ∈ R 3×3 are identity and null matrices, and H( ) depends on the parametrization used to describe the orientation [1]. The rate of change of l i ,l i , can be computed as the projection of the velocity of point A i along the i-th cable direction t i [1], [23], [24], that is:…”

Section: A Differential Kinematicsmentioning

confidence: 99%

“…Since the natural oscillation frequencies characterize the free motion of the EE about equilibria (l = l 0 ,l =l = 0 n×1 ), it is useful to express (24) in terms of the λ DoFs that the EE preserves and their derivatives, ζ f ,ζ f ,ζ f . This is achieved by considering (2) for i = 1, • • • , n and a fixed l 0 , as well as ( 23) and its time derivative:…”

Section: B Free-motion Dynamicsmentioning

confidence: 99%

“…time. The free motion internal dynamics of the EE can be obtained by substituting (26) in (24) and left-multiplying by Ξ ⊥ T . Since Ξ ⊥ T Ξ T = 0 λ×n , then:…”

Section: B Free-motion Dynamicsmentioning

confidence: 99%

See 2 more Smart Citations

Natural Oscillations of Underactuated Cable-Driven Parallel Robots

2021

View full text Add to dashboard Cite

Underactuated Cable-Driven Parallel Robots (CDPR) employ a number of cables smaller than the degrees of freedom (DoFs) of the end-effector (EE) that they control. As a consequence, the EE is underconstrained and preserves some freedoms even when all actuators are locked, which may lead to undesirable oscillations. This paper proposes a methodology for the computation of the EE natural oscillation frequencies, whose knowledge has proven to be convenient for control purposes. This procedure, based on the linearization of the system internal dynamics about equilibrium configurations, can be applied to a generic robot suspended by any number of cables comprised between 2 and 5. The kinematics, dynamics, stability and stiffness of the robot free motion are investigated in detail. The validity of the proposed method is demonstrated by experiments on 6-DoF prototypes actuated by 2, 3, and 4 cables. Additionally, in order to highlight the interest in a robotic context, this modelling strategy is applied to the trajectory planning of a 6-DoF 4-cable CDPR by means of a frequency-based method (multi-mode input shaping), and the latter is experimentally compared with traditional non-frequency-based motion planners.

show abstract

Section: A Differential Kinematicsmentioning

confidence: 99%

Section: B Free-motion Dynamicsmentioning

confidence: 99%

See 1 more Smart Citation

Natural Oscillations of Underactuated Cable-Driven Parallel Robots

2021

View full text Add to dashboard Cite

show abstract

“…The use of the proposed end-effector should be investigated by conducting the workspace analysis and stiffness analysis for CDPRs as the workspace analysis of CDPRs has been conducted considering feasible tension distributions for various CDPRs [11][12][13][14]. In addition, the stiffness analysis of CDPRs has been researched for several CDPRs [15][16][17][18]. Therefore, in this paper, for addressing the cable interference problem with maximizing the workspace volume while providing vertical stiffness, a novel retractable beam type end-effector with the guide pulleys distributed in a single horizontal plane is proposed for a 3D-printing CDPR as shown in Figure 4.…”

Section: Introductionmentioning

confidence: 99%

Workspace and Stiffness Analysis of 3D Printing Cable-Driven Parallel Robot with a Retractable Beam-Type End-Effector

Jung

2020

Robotics

View full text Add to dashboard Cite

3D printing is a widely used technology that has been recently applied in construction to reduce construction time significantly. A large 3D printer often uses a traditional Cartesian robot with inherent problems, such as position errors and printing nozzle vibrations, due to the long, heavy horizontal beam carrying it and a large amount of power required to actuate the heavy beam. A cable-driven parallel robot (CDPR) can be a good alternative system to reduce the vibrations and necessary power because the robot’s lightweight cables can manipulate the printing nozzle. However, a large 3D printing CDPR should be carefully designed to maximize the workspace and avoid cable interference. It also needs to be stiff enough to reject disturbances from the environment properly. A CDPR with a retractable beam-type end-effector with cables through the guide pulleys in a single plane is suggested for avoiding cable interference while maximizing the workspace. The effects of using the retractable end-effector on the workspace were analyzed relative to the cable connection points’ location changes. Static stiffness analysis was conducted to examine the natural frequencies, and the geometric parameters of the end-effector were adjusted to improve the lowest natural frequencies. Simulation results show that a retractable beam-type end-effector can effectively expand the wrench-feasible workspace.

show abstract

“…One example of the latter case is provided by crane-type manipulators [8,9], in which gravity plays the role of an additional virtual cable. A rich literature exists for fully constrained robots, whose features have been studied under several viewpoints, including workspace analysis [10][11][12][13][14][15][16][17], stiffness [18,19], cable interference [20,21], optimal design [22,23], etc. Conversely, underconstrained CDPRs have received little attention in the literature [24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra

Fu¹,

Yang²,

Yang

2013

Journal of Mechanisms and Robotics

View full text Add to dashboard Cite

In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

show abstract

Geometric Stiffness Analysis of Wire Robots: A Mechanical Approach

Cited by 21 publications

References 12 publications

Natural Oscillations of Underactuated Cable-Driven Parallel Robots

Natural Oscillations of Underactuated Cable-Driven Parallel Robots

Workspace and Stiffness Analysis of 3D Printing Cable-Driven Parallel Robot with a Retractable Beam-Type End-Effector

Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra

Contact Info

Product

Resources

About