Examination and comparison of different methods to model closed loop kinematic chains using Lagrangian formulation with cut joint, clearance joint constraint and elastic joint approaches

Marques, Filipe; Roupa, Ivo; Silva, Miguel T.; Flores, Paulo; Lankarani, Hamid M.

doi:10.1016/j.mechmachtheory.2021.104294

Cited by 33 publications

(4 citation statements)

References 94 publications

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“…where t m is the tangential unit vector of potential contact point m and rd m is the radius vector of potential contact points m. Spherical joint only appears point contact state, contact force and moment can be calculated through equations (12), (14), and (15). Detection of the instant of contact is correlated with the penetration depth of two discrete integration steps t n and t nþ1 .…”

Section: Calculation Of Contact Force For Clearances Jointsmentioning

confidence: 99%

“…Here, note that the normal force does not produce torque. The friction torque acting on the clearance joint should be calculated according to equation (15).…”

Section: Calculation Of Contact Force For Clearances Jointsmentioning

confidence: 99%

“…Wu et al 13 studied the nonlinear characteristics of a crank-slider mechanism with multiple clearance joints through correlation dimensions. Ambrósio and Pombo 14 and Marques et al 15 improved pre-existing dynamic modeling methods of the mechanisms containing clearance joint, respectively. Both of these methods simplify the modeling process and improve modeling efficiency.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic response analysis for multi-degrees-of-freedom parallel mechanisms with various types of three-dimensional clearance joints

Jia

Chen

2021

International Journal of Advanced Robotic Systems

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For spatial multibody systems, the dynamic equations of multibody systems with compound clearance joints have a high level of nonlinearity. The coupling between different types of clearance joints may lead to abundant dynamic behavior. At present, the dynamic response analysis of the spatial parallel mechanism considering the three-dimensional (3D) compound clearance joint has not been reported. This work proposes a modeling method to investigate the influence of the 3D compound clearance joint on the dynamics characteristics of the spatial parallel mechanism. For this purpose, 3D kinematic models of spherical clearance joint and revolute joint with radial and axial clearances are derived. Contact force is described as normal contact and tangential friction and later introduced into the nonlinear dynamics model, which is established by the Lagrange multiplier technique and Jacobian of constraint matrix. The influences of compound clearance joint and initial misalignment of bearing axes on the system are analyzed. Furthermore, validation of dynamics model is evaluated by ADAMS and Newton–Euler method. This work provides an essential theoretical basis for studying the influences of 3D clearance joints on dynamic responses and nonlinear behavior of parallel mechanisms.

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Section: Calculation Of Contact Force For Clearances Jointsmentioning

confidence: 99%

“…Here, note that the normal force does not produce torque. The friction torque acting on the clearance joint should be calculated according to equation (15).…”

Section: Calculation Of Contact Force For Clearances Jointsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamic response analysis for multi-degrees-of-freedom parallel mechanisms with various types of three-dimensional clearance joints

Jia

Chen

2021

International Journal of Advanced Robotic Systems

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“…For the control scheme design, the dynamic model must be efficient enough for the real-time calculation; for the structural design, it is necessary to calculate the driving forces/torque and the constrained forces/moments simultaneously [18]. In general, dynamic modeling methods [19][20][21] can be divided into four categories: Lagrangian formula [22,23], Newton-Euler method [18,24,25], virtual work principle [26,27], and Kane equation [28]. Among them, the Lagrangian formula is advantageous in solving the driving force of manipulator, with its explicit dynamic form conducive to dynamic analysis and control.…”

Section: Introductionmentioning

confidence: 99%

Kinematic and dynamic analysis of a 4-DOF over-constraint parallel driving mechanism with planar sub-closed chains

et al. 2023

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In this paper, a new over-constrained parallel driving mechanism (PDM) with planar sub-closed chains is proposed. First, the number of over-constraints on the PDM is calculated. Then, an analysis is conducted as to the kinematics of the hybrid manipulator, including positions, velocities, and accelerations of all bodies. Furthermore, the Newton–Euler approach is taken to deduce the kinematic formula of each link and the formula of inertial force at the center of mass. However, it remains difficult to solve the equation since the number of equations is smaller than that of unknown variables. To solve this problem, the screw theory is applied in the present study to analyze the cause of over-constraints, with the link’s elastic deformation introduced as the supplement of deformation compatibility equations. Moreover, the actuation forces and constrained forces/moments are calculated simultaneously. Finally, the dynamic model is verified through simulation and experimentation. The proposed modeling approach provides a fundamental basis for the structural optimization and friction force computation of the over-constrained PDM.

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Vibrations of a Rigid Hanged by an Elastic Kinematic Chain and a Rigid Kinematic Chain

Stan

Nicolae²,

Stănescu³

2022

Springer Proceedings in Physics

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Examination and comparison of different methods to model closed loop kinematic chains using Lagrangian formulation with cut joint, clearance joint constraint and elastic joint approaches

Cited by 33 publications

References 94 publications

Dynamic response analysis for multi-degrees-of-freedom parallel mechanisms with various types of three-dimensional clearance joints

Dynamic response analysis for multi-degrees-of-freedom parallel mechanisms with various types of three-dimensional clearance joints

Kinematic and dynamic analysis of a 4-DOF over-constraint parallel driving mechanism with planar sub-closed chains

Vibrations of a Rigid Hanged by an Elastic Kinematic Chain and a Rigid Kinematic Chain

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