A Lie Group Approach to the Modular Modeling of Kinematically Non-Redundant Parallel Mechanisms

2019 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Lie Group ◽  
Robotic Systems ◽  
Parallel Mechanisms ◽  
Parallel Kinematics ◽  
Task Space ◽  
Group Approach ◽  
Modular Modeling ◽  
Modeling Approach ◽  
And Topology ◽  
Space Formulation

Abstract Parallel kinematics manupulators (PKM) are established robotic systems. Yet there is no established modeling approach that takes into account the special kinematics of the (usually structurally identical) limbs. In this paper a modeling approach is proposed that accounts for the special kinematics and topology of PKM. It makes use of modern Lie group formulations for rigid body systems that admits efficient description independent of modeling conventions. A task space formulation is presented that can be directly used for model-based control purposes.

scholarly journals Constraint and Mobility Change Analysis of Rubik’s Cube-inspired Reconfigurable Joints and Corresponding Parallel Mechanisms

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Duanling Li ◽  
Pu Jia ◽  
Jiazhou Li ◽  
Dan Zhang ◽  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Unique Feature ◽  
Theoretical Method ◽  
Geometric Constraint ◽  
Parallel Mechanisms ◽  
Change Analysis ◽  
Application Range ◽  
And Topology ◽  
Physical Experiments ◽  
Underlying Principle

Abstract The current research of reconfigurable parallel mechanism mainly focuses on the construction of reconfigurable joints. Compared with the method of changing the mobility by physical locking joints, the geometric constraint has good controllability, and the constructed parallel mechanism has more configurations and wider application range. This paper presents a reconfigurable axis (rA) joint inspired and evolved from Rubik's Cubes, which have a unique feature of geometric and physical constraint of axes of joint. The effectiveness of the rA joint in the construction of the limb is analyzed, resulting in a change in mobility and topology of the parallel mechanism. The rA joint makes the angle among the three axes inside the groove changed arbitrarily. This change in mobility is completed by the case illustrated by a 3(rA)P(rA) reconfigurable parallel mechanism having variable mobility from 1 to 6 and having various special configurations including pure translations, pure rotations. The underlying principle of the metamorphosis of this rA joint is shown by investigating the dependence of the corresponding screw system comprising of line vectors, leading to evolution of the rA joint from two types of spherical joints to three types of variable Hooke joints and one revolute joint. The reconfigurable parallel mechanism alters its topology by rotating or locking the axis of rA joint to turn all limbs into different phases. The prototype of reconfigurable parallel mechanism is manufactured and all configurations are enumerated to verify the validity of the theoretical method by physical experiments.

scholarly journals Generalized Hamiltonian biodynamics and topology invariants of humanoid robots

2002 ◽  
Vol 31 (9) ◽  
pp. 555-565 ◽  
Author(s):  
Vladimir Ivancevic
Keyword(s):  
Phase Space ◽  
Lie Group ◽  
Humanoid Robots ◽  
And Topology ◽  
Hamiltonian Model

Humanoid robots are anthropomorphic mechanisms with biodynamics that resembles human musculo-skeletal dynamics. This paper proposes a new generalized (dissipative, muscle-driven, stochastic) Hamiltonian model of humanoid biodynamics. Also, (co)homological analysis is performed on its Lie-group based configuration and momentum phase-space manifolds.

Rigid Registration of Point Clouds Based on Indirect Lie Group Approach

2019 ◽  
Author(s):  
Liliane Rodrigues de Almeida ◽  
Gilson Antonio Giraldi ◽  
Marcelo Bernardes Vieira
Keyword(s):  
Lie Group ◽  
Point Clouds ◽  
Group Approach ◽  
Rigid Registration

scholarly journals Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Z. E. Musielak ◽  
N. Davachi ◽  
M. Rosario-Franco
Keyword(s):  
Differential Equations ◽  
Lie Groups ◽  
Lie Group ◽  
Algebraic Structure ◽  
Second Order ◽  
Lagrangian Formalism ◽  
Group Approach ◽  
Second Order Differential Equations ◽  
Gauge Functions ◽  
The Relationship

A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate novel equations. The Lagrangian formalism based on standard, null, and nonstandard Lagrangians is established for all members of the semigroup. For the null Lagrangians, their corresponding gauge functions are derived. The obtained Lagrangians are either new or generalization of those previously known. The previously developed Lie group approach to derive some equations of the semigroup is also described. It is shown that certain equations of the semigroup cannot be factorized, and therefore, their Lie groups cannot be determined. A possible solution of this problem is proposed, and the relationship between the Lagrangian formalism and the Lie group approach is discussed.

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