A mathematical method for ergonomic-based design: Placement

Karim Abdel-Malek, Wei Yu, Jingzhou Yang, Kyle Nebel

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


A rigorous mathematical formulation for ergonomic design based on obtaining and visualizing the workspace of human limbs is herein presented. The methodology and formulation presented in this paper are aimed at placing the human with respect to specified targets, whereby optimizing a given human performance measure. These measures are developed as mathematical cost functions that can be maximized or minimized. For example, as a result of this analysis, a method for placing the human operator relative to the controls in an assembly line while minimizing the person's stress at each joint can be achieved. Other cost functions such as maximizing reachability or maximizing dexterity are considered. The method is characterized by two steps: (1) determine the boundary envelope (also called reach envelope) of a human limb in closed form as, and, (2) move the workspace envelope towards optimizing the cost function while satisfying all constraints. By defining a new position and orientation of the limb's workspace with respect to the target points, it is possible to establish an ergonomic design that satisfies the given constraints. The strengths of this method are in its ability to visualize the placement-reach design problem and in its broadly applicable mathematical formulation well suited for computer implementation. Furthermore, because the ergonomic design problem is indeed an optimization process, the use of optimization techniques in this work lends itself to addressing other standing problems. The formulation and code are demonstrated using a number of examples.

Original languageEnglish
Pages (from-to)375-394
Number of pages20
JournalInternational Journal of Industrial Ergonomics
Issue number5
StatePublished - Nov 2004


  • Ergonomic design
  • Optimization
  • Placement
  • Reach envelope
  • Reachability


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