Abstract
An inverse dynamics and kinematics of a flexible manipulator is derived in symbolic form based on the recursive Lagrangian assumed mode method. A PC-based program has implemented the algorithm to automatically generate the inverse dynamics and kinematics for an elastic robot in a symbolic form. A case study is given to illustrate how to use this program for inverse dynamic and kinematic generation. Simulation results for a case study by considering different mode shape are compared with the rigid case.
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Abbreviations
- A i :
-
joint transformation relates systemi to systemi-1
- E i :
-
link transformation relates the deflection of systemi to systemi
- F i :
-
joint torque acting on jointi
- g:
-
gravity vector expressed at the base coordinates
- J :
-
inertia =\(\left[ {\begin{array}{*{20}c} {\left[ {J_{jh} } \right]} & {\left[ {J_{jhk} } \right]} \\ {\left[ {J_{hjk} } \right]} & {\left[ {J_{jfhk} } \right]} \\ \end{array} } \right]\)
- K :
-
kinetic energy of the system
- l i :
-
length of linki
- M i :
-
a mass concentrated at the joint i
- m i :
-
number of modes used to describe the deflection of link i
- n :
-
number of links
- q h :
-
joint variable of thehth joint
- q hk :
-
time-varying amplitude of mode k of link h
- R :
-
vector of remaining dynamics and external forcing terms =\(\left[ {R_1 ,R_2 ,..., R_h ..., R_n , R_{11} ,R_{12} ..., R_{1m_1 } , R_{21} ..., R_{2m_2 } ..., R_{h1} ..., R_{hm_n } ..., R_{nm_n } } \right]^T \)
- r i :
-
vector locating the centre of mass of linki
- R j :
-
dynamics from the joint equation j, excluding second derivatives of the generalized coordinates
- R if :
-
dynamics from the deflection equation jf, excluding second derivatives of the generalized coordinates
- V :
-
potential energy
- W i :
-
transformation from the base to theith link
- \(\hat W_i \) :
-
transformation from the base to the systemî
- z :
-
the vector of generalised coordinates =\(\left[ {q_1 , q_2 ,..., q_h ..., q_n , q_{11} , q_{12} ..., q_{1m_1 } , q_{21} ..., q_{2m_2 } ..., q_{h1} ..., q_{hm_n } ..., q_{nm_n } } \right]^T \)
- μ:
-
link density
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Korayem, M.H., Yao, Y. & Basu, A. Application of symbolic manipulation to inverse dynamics and kinematics of elastic robots. Int J Adv Manuf Technol 9, 343–350 (1994). https://doi.org/10.1007/BF01781288
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DOI: https://doi.org/10.1007/BF01781288