Tolerance Design of Robot Parameters Using Generalized Reduced Gradient Algorithm

Abstract

Abstract-In robot design, how to allocate tolerances for parts in manufacturing and assembling of robot is very important because this directly affects product quality and manufacturing cost. This paper introduces a technique using the Generalized Reduced Gradient algorithm optimization to allocate tolerances into robot parts. This method consists of three steps. First, based on the particular structure of robot, various methods are considered before the best method suitable for modeling the associated equation is chosen. Then, a mathematical model for tolerance allocation is formulated and transferred into the non-linear multi-variable optimization problem. Finally, this optimization problem is solved by using the Generalized Reduced Gradient algorithm. Two examples are used to verify the feasibility of the proposed method; the accuracy and effectiveness of the proposed method in producing the tolerance allocations is also illustrated via calculation and simulation results.

Tolerance Synthesis of Delta-like Parallel Robots Using a Nonlinear Optimisation Method

“…A local uniqueness hypothesis for reliably obtaining pose error upper limits using nonlinear optimisation was proposed in [20]. Trang et al [21] introduced a technique using the generalised reduced gradient algorithm optimisation to allocate tolerances into robot parts. By using the Denavit-Hartenberg (DH) rule for modelling the kinematic problem in that study, a mathematical model for tolerance allocation was developed and used in the nonlinear multivariable optimisation problem.…”

Investigating workspace and positional accuracy in 3 Degrees of Freedom planar manipulator under the link tolerances

“…Investigation of mechanical error in closed chain four-bar mechanism under the effects of link tolerance is presented by author wherein geometrical approach is utilized. 32…”

“…The prominent amongst them are joint clearances, backlash, design tolerance and assembly error. 2,[22][23][24][25][26][27][28][29][30][31][32][33][34] Analysis of joint clearances is modelled in multi-loop mechanisms and is presented by Ming-June Tsai et al 22 The effect of geometric error on positioning precision is studied by Henrique et al 23 A general method to solve effect of uncertainty due to manufacturing and assembly error as design problem is suggested. Further, the uncertainty due to joint clearance is modelled and analysed for the planar and spatial robots and is presented by Zhu et al 24 The error modelling of inherent uncertainties of a planar 3-RRR parallel manipulator like manufacturing tolerances, input errors and joint clearances along with validation of model is proposed by Zhan Zhenhui et al 25 to solve a motion reliability problem.…”

“…A three-step methodology for dimensional tolerance synthesis of a 2-DoF and a 3-DoF parallel manipulator is presented by Goldsztejn et al 29 A novel approach for kinematic reliability analysis of planar parallel manipulators based on error propagation on plane motion groups and clipped Gaussian in terms of joint clearance, input uncertainty and manufacturing imperfection is proposed by Zhao et al 30 The modelling of link tolerances as source of mechanical error is presented in literature. 31,32 Amongst these, the link tolerances being inevitable and is measurable at assembly stage, the resulting pose errors are possible to estimate. The manipulators are possible to design to overcome these error by proper tolerance design, and by correction through drive input.…”

“…Investigation of mechanical error in closed chain four-bar mechanism under the effects of link tolerance is presented by author wherein geometrical approach is utilized. 32 The tolerance being unavoidable, the extent of deviations needed to be studied. In this paper, the workspace is investigated by taking different parameters and uncertainty in the manipulator.…”