A Variational Approach for Modeling Flexibility Effects in Manipulator Arms

Abstract

SUMMARYThis paper presents a general technique to model flexible components (mainly links and joints flexibilities are considered) of manipulator arms based on Castigliano's theorem of least work. The robotic arms flexibility properties are derived and represented by the matrix of compliance coefficients. Such expressions can be used to determine the errors due to the robotic tip deformations under the application of a set of applied loads at the tip in a Cartesian space. Once these deformations are computed, they may be used to correct for the positional errors arisen from the robotic structural deformations in the motion control algorithms.

Accurate nonlinear modeling for flexible manipulators using mixed finite element formulation in order to obtain maximum allowable load

“…Lagrangian dynamics has been utilized in conjunction with the assumed modes method to derive equations of motion. Meghdari [3] has presented a general technique to model flexible components of robotic arms based on Castigliano's theorem. The flexibility properties of the manipulator arms are derived and represented by a matrix of compliance coefficients.…”

Quasi-Static Deflection Compensation Control of Flexible Manipulator

“…The mathematical model will be derived using a variational method based on Castigliano's theorem of least work (CTLW) [6]. It will be shown that minimum two strain gages per link are needed to monitor deflections subjected to bending in a plane.…”

“…The axial deflection is cause by axial force Fa and it is described by axial displacement &a as shown in Figure 3. The magnitude of axial bending deflection is relatively small compared with the torsional and bending deflections in manipulator applications, hence the axial deflection is neglected in most of previous research [5,6,12]. Only the bending deflection in a plane is investigated in this project.…”

“…In the second category, the deflections of the flexible links are calculated using 2 some mathematical models, then a kinematic model is used to calibrate the control system to compensate the deflections. Most previous works in this category require that the exact payloads and dimensions of the links must be known ahead to calculate the deflections [ 6,7]. This is very difficult in the real applications where the manipulator links have complex shapes and the payloads vary from task to task.…”

“…Finite Element Method has been utilized by many researchers to model the deflections of the flexible manipulator links [7,8,9]. Kanoh [6]. He considers the entire serial chain of the flexible links as a whole structure, then CTL W is applied to determine the deformation of the whole structure.…”