MA1-Parametric Modeling and Optimization of Precision Machines and Systems

Dr. Martin L. Culpepper (Massachusetts Institute of Technology)

Monday, October 26, 2026 (1:30 PM – 5:30 PM)

This tutorial covers key principles and best practices that are required to parametrically model and optimize precision machines/systems via Homogeneous Transformation Matrices (HTMs).  We cover (i) how to model component-level errors that manifest from compliance, thermal, fabrication, assembly, and other sources; (ii) how to combine the component-level errors into a system/machine-level error model, and (iii) how to use that model to rapidly converge on an optimized design that yields desired performance while minimizing the cost.  Participants will learn how to use these models to predict a machine’s/system’s nominal performance, the sensitivity of its performance to design variables, and how to estimate variations from nominal performance.  Case studies will be presented over a range of applications including optical systems, manufacturing equipment, positioning stages and metrology equipment.  This tutorial is very hands on.  Throughout the tutorial, participants will work on creating the parts of parametric models for sub-systems via Microsoft Excel.  Participants will then (i) build confidence by creating their own system-level model of a machine; and then (ii) use that model to optimize the machine’s/system’s performance relative to constraints, e.g., cost, schedule and envelope.

Learning Outcomes

You will learn about the following:

1. Principles of HTM analysis, including mathematical and practical understanding of what they are and how they should be used, how to populate HTMs with errors that are parametrically linked to machine design and cost, and how to combine them to model a system’s cost and performance characteristics.
2. How to parametrically model the nominal and stochastic behavior of a variety of common errors that must be dealt with in precision machines, and how to properly understand that process, and model outputs, relative to deterministic precision engineering design practices
3. How to create sub-system and system-level parametric models that may be used to maximize the ratio of cost to performance in precision machines and systems.
4. How to use these models to generate key data sets for making, and communicating, engineering and financial decision.

Note: Ideally participants bring their own laptops, equipped with Microsoft Excel, for use during the hands-on modeling and analysis exercises.  A laptop is not required, as participants can follow on with another participant, but a laptop is highly recommended.