A More General Mobility Criterion for Parallel Platforms

Rico, José M.; Aguilera, L. D.; Gallardo, Jaime; Rodríguez, Ramón López; Orozco, Horacio; Barrera, Juan Manuel

doi:10.1115/1.2118687

Cited by 32 publications

(17 citation statements)

References 13 publications

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“…Taking into account that the SPM is composed of seven links, two revolute pairs, two prismatic pairs, one universal joint, and three spherical joints, then the resulting dof of the proposed SPM is three. Moreover, it can be shown that this SPM is an exceptional platform according with the classification proposed in Rico et al [20].…”

Section: A Family Of Spms Composed Of Two Legsmentioning

confidence: 94%

A family of spherical parallel manipulators with two legs

Gallardo

Rodríguez

Caudillo

et al. 2008

Mechanism and Machine Theory

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Section: A Family Of Spms Composed Of Two Legsmentioning

confidence: 94%

A family of spherical parallel manipulators with two legs

Gallardo

Rodríguez

Caudillo

et al. 2008

Mechanism and Machine Theory

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“…The mobility can also be found by the motion space as in Rico et al [6] [7]. The degree of freedom of the motion of the end effector is first found.…”

Section: Introductionmentioning

confidence: 99%

“…First, we use Grübler's formula or a generic method based on the results in Rico et al [6] [7] to verify whether the manipulator, considering the passive joints only, generates a non-trivial motion. This is based on the results found in From and Gravdahl [14].…”

Section: Introductionmentioning

confidence: 99%

A Geometric Approach to the Design of Serial and Parallel Manipulators with Passive Joints

Pham¹,

From²,

Gravdahl³

2014

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The use of robotic manipulators in remote and sensitive areas calls for more robust solutions when handling joint failure, and the industry demands mathematically robust approaches to handle even the worst case scenarios. For both serial and parallel manipulators torque failure is indeed a worst case scenario. Thus, a systematic analysis of the effects of external forces on manipulators with passive joints is presented. For serial manipulators we find under what conditions the robot is conditionally equilibrated, that is, equilibrated with respect to a specific external force. These conditions are, as expected, very restrictive. The serial, or subchain, case serves as a good platform for analyzing parallel manipulators. In parallel manipulators passive joints can appear as a design choice or as a result of torque failure. In both cases a good understanding of the effects that passive joints have on the mobility and motion of the parallel manipulator is crucial. We first look at the effects that passive joints have on the mobility of the mechanism. Then, if the mobility considering passive joints only is not zero we find a condition similar to the serial case for which the parallel manipulator is conditionally equilibrated with respect to a specific external force.

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“…Li et al implemented Herve's theory (under the name of displacement manifold) in classification and synthesis of 5 dof parallel mechanisms [15]. On the mobility analysis side, Rico's work on single closed loop [16] and parallel mechanisms [17] are also applications of Herve's theory. However, Rico's work was less general and thus did not gain much popularity in comparison to screw theory based method.…”

mentioning

confidence: 97%

Equivalence relation and partial ordering of parallel mechanisms with applications to mechanism synthesis and mobility analysis

Ding

2010

Chin. Sci. Bull.

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Motion type (or motion pattern) of a mechanism is defined as the set of all rigid motions achievable by the mechanism's end-effector; the motion type of a parallel mechanism equals the intersection set of all subchain motion types. The motion type of a non-instantaneous parallel mechanism locally agrees with a regular submanifold (or a Lie subgroup in particular) of the special Euclidean group SE(3). Based on submanifold germs of SE (3), we can define an equivalence relation and a partial order relation for both motion types and parallel mechanisms: two motion types are equivalent if and only if they agree on an open neighborhood around the identity element of SE (3); two motion types are comparable if and only if one is a submanifold of the other on an open neighborhood around the identity of SE(3). It is also possible to define equivalence relation and partial ordering on the collection of parallel mechanisms. In this paper, we first study properties of the equivalence and partial order relation of both motion types and parallel mechanisms, then we discuss their application in type synthesis, mobility analysis and non-overconstrained ness realization of parallel mechanisms. parallel mechanism, motion type, equivalence relation, partial order relation, mechanism synthesis, mobility analysis Citation:Wu Y Q, Ding H. Equivalence relation and partial ordering of parallel mechanisms with applications to mechanism synthesis and mobility analysis.

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A More General Mobility Criterion for Parallel Platforms

Cited by 32 publications

References 13 publications

A family of spherical parallel manipulators with two legs

A family of spherical parallel manipulators with two legs

A Geometric Approach to the Design of Serial and Parallel Manipulators with Passive Joints

Equivalence relation and partial ordering of parallel mechanisms with applications to mechanism synthesis and mobility analysis

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