Abstract
Considering the complex dynamic modeling of multi‐DOF planar flexible manipulators, a general‐purpose method for the rigid‐flexible coupling dynamic modeling of N‐DOF flexible manipulators is proposed in this paper, and symbolic calculation software is developed. The modeling method is based on the Lagrange equation and assumed mode method (AMM). First, the N‐DOF flexible manipulator is divided into two parts, which are assumed to be rigid and flexible. On this basis, the rigid part and the flexible part are coupled, and the calculation process of the model is further simplified. Then, the simplest general symbolic expression of the dynamic model of the N‐DOF flexible manipulator is obtained with the induction method. According to the modeling method, “symbolic expression computation software for dynamic equations of N‐DOF flexible manipulators” is developed using the symbolic calculation software Mathematica. Finally, the dynamic modeling method and the symbolic calculation software are verified by a trajectory tracking experiment with a PD control applied to a 2‐DOF flexible manipulator. Compared with the traditional modeling method, the calculation time can be reduced by more than 90% using the modeling method proposed in this paper, which significantly reduces the complexity of the modeling process.
Highlights
Robotic manipulators are widely used in environments that are hazardous to humans and in situations where there are substantial amounts of repetitive work to reduce the burden on humans and to assist in accomplishing special tasks
From equations (24) and (25), we find that there are not otfcroeiongrrulmimydpslarimtniwigogoiindttthieoθ_rmnfim€fo_iλsiθ_tλ,ii.oθwi_nNnjhoaaitctdneahrddbmisltyhris,oiogntwuihdliedttorhmheta€θohavitreeieobcbnnuoeotueanpaflnlledisfn_xoiigλflbffle_lteexjeλxrid.bmibelelfseoilbrsimmenmtkowaatteiidkooeeennnssolving the dynamic equations easier, and this is an important reason for establishing such float frames to describe the flexible-link manipulators (FLMs)
A general modeling method for the dynamic equations of an N-DOF exible manipulator based on the Lagrange equation
Summary
Robotic manipulators are widely used in environments that are hazardous to humans and in situations where there are substantial amounts of repetitive work to reduce the burden on humans and to assist in accomplishing special tasks. In human-robot interactions, a lightweight FLM is safer to humans and has smaller workload requirements on joint drivers, sensors [13, 14], etc Such an FLM experiences vibration and elastic deformation during movement, which will greatly affect the stability of the entire system and the positioning accuracy of the end [15, 16]. Considering the payload mass at the end of the manipulator and the lumped mass (for example, the mass of the actuators) on each link, multi-DOF rigid-flexible coupling dynamic modeling is more complicated. Considering the complexity of the dynamic modeling of multi-DOF FLMs with a lumped mass on the links, a general-purpose dynamic modeling method for N-DOF FLMs based on the Lagrange equation is presented in this paper, and the symbolic expression computation software for the dynamic equations of N-DOF flexible manipulators is developed.
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