Modelling and index analysis of a Delta-type mechanism

Hsu, Kuei-Shu; Karkoub, Mansour; Tsai, Ming-Han; Her, Ming-Guo

doi:10.1243/1464419042035944

Cited by 8 publications

(6 citation statements)

References 11 publications

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“…While equation 4is used for obtaining the dynamical model in the next section, calculating the mentioned kinematics is not the objective in this work and therefore is skipped. See Williams 21 and Hsu et al 22 for detailed solution and further analysis of the kinematics of the robot.…”

Section: Kinematicsmentioning

confidence: 99%

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Analytical dynamic modeling of Delta robot with experimental verification

Asadi

Heydari

2020

Proceedings of the Institution of Mechanical Engineers, Part K:

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In this paper, an explicit dynamic model of Delta robot is obtained analytically. The main contribution of this work is that, unlike existing prior work, the final dynamics model is given directly in the form of [Formula: see text], with explicit expressions for M, C and G. This is of great importance, since many advanced control techniques like Optimal Control need dynamic model in an explicit form, i.e. time derivative of state vector given explicitly in terms of the states and control vectors. To this goal, first, velocity and acceleration analysis is done by differentiating robot's geometrical loops directly. Then, Jacobian matrices are calculated to have kinematic relations in a more compact form. After that, principle of virtual work is implemented to derive the dynamic equations. In this part, Jacobian matrices are substituted into dynamic model. This is unlike other referenced works on Delta robot dynamics that need to continue the derivation in symbolic software or derive the model implicitly. Using Jacobians, dramatically simplifies the final explicit dynamic model. Therefore, the final dynamic equations are calculated in a straightforward manner without any use of symbolic calculation software. After all, the presented model is verified with an experimental setup. The model shows good accuracy in terms of torque prediction.

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Section: Kinematicsmentioning

confidence: 99%

“…See Williams 21 and Hsu et al. 22 for detailed solution and further analysis of the kinematics of the robot.…”

Section: Kinematicsmentioning

confidence: 99%

Analytical dynamic modeling of Delta robot with experimental verification

Asadi

Heydari

2020

Proceedings of the Institution of Mechanical Engineers, Part K:

View full text Add to dashboard Cite

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“…Another term one encounters in this setting is "redundant DOF" (Zhang et al, 2003), which however may lead to confusion as the term redundant DOF is used in robotics for robots featuring a greater number of actuators than necessary for a given task space which allows for special control movements (such as the human arm having seven relative joint motions for six DOFs at the hand). In some cases the term "parasitic DOF" is used for isolated DOFs (Rolland, 1999); however, the term "parasitic motion" (Carretero et al, 2000) or "parasitic DOF" is also (and more frequently) used to describe unwanted dependent motions in some direction such as the vertical axis of a lower mobility platform (Hsu et al, 2004;Isaksson et al, 2015;Merlet, 2005). As a further variant one finds the term parasitic degrees of freedom meaning additional degrees of freedom added to the principal DOFs by compliant joints (Togashi et al, 2014).…”

Section: Types Of Isolated Degrees Of Freedommentioning

confidence: 99%

Solving the double-banana rigidity problem: a loop-based approach

2016

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Abstract. Rigidity detection is an important tool for structural synthesis of mechanisms, as it helps to unveil possible sources of inconsistency in Grübler's count of degrees of freedom (DOFs) and thus to generate consistent kinematical models of complex mechanisms. One case that has puzzled researchers over many decades is the famous "double-banana" problem, which is a representative counter-example of Laman's rigidity condition formula for which existing standard DOF counting formulas fail. The reason for this is the body-by-body and joint-by-joint decomposition of the interconnection structure in classical algorithms, which does not unveil structural isotropy groups for example when whole substructures rotate about an "implied hinge" according to Streinu. In this paper, a completely new approach for rigidity detection for cases as the "double-banana" counterexample in which bars are connected by spherical joints is presented. The novelty of the approach consists in regarding the structure not as a set of joint-connected bodies but as a set of interconnected loops. By tracking isolated DOFs such as those arising between pairs of spherical joints, rigidity/mobility subspaces can be easily identified and thus the "double-banana" paradox can be resolved. Although the paper focuses on the solution of the double-banana mechanism as a special case of paradox bar-and-joint frameworks, the procedure is valid for general body-and-joint mechanisms, as is shown by the decomposition of spherical joints into a series of revolute joints and their rigid-link interconnections.

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“…24 In many applications, the analysis of kinematic chain requires iterative approaches such as Newton-Raphson method, which is a computationally expensive practice. 25,26 In that sense, a major problem in the kinematics analysis is to formulate solution algorithms that do not contain nested vector loops, and hence simplify the kinematic computations. Among the existing studies, the most straightforward approach is to adopt a geometry-based derivation of kinematics equations with exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Unified Kinematics of Prismatically Actuated Parallel Delta Robots

et al. 2019

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SummaryThis paper presents a unified formulation for the kinematics, singularity and workspace analyses of parallel delta robots with prismatic actuation. Unlike the existing studies, the derivations presented in this paper are made by assuming variable angles and variable link lengths. Thus, the presented scheme can be used for all of the possible linear delta robot configurations including the ones with asymmetric kinematic chains. Referring to a geometry-based derivation, the paper first formulates the position and the velocity kinematics of linear delta robots with non-iterative exact solutions. Then, all of the singular configurations are identified assuming a parametric content for the Jacobian matrix derived in the velocity kinematics section. Furthermore, a benchmark study is carried out to determine the linear delta robot configuration with the maximum cubic workspace among symmetric and semi-symmetric kinematic chains. In order to show the validity of the proposed approach, two sets of experiments are made, respectively, on the horizontal and the Keops type of linear delta robots. The experiment results for the confirmation of the presented kinematic analysis and the simulation results for the determination of the maximum cubic workspace illustrate the efficacy and the flexible applicability of the proposed framework.

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Modelling and index analysis of a Delta-type mechanism

Cited by 8 publications

References 11 publications

Analytical dynamic modeling of Delta robot with experimental verification

Analytical dynamic modeling of Delta robot with experimental verification

Solving the double-banana rigidity problem: a loop-based approach

Unified Kinematics of Prismatically Actuated Parallel Delta Robots

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