Originating NASA educational account. Sections Angle of Attack and Aerodynamic Center distinguish the nearly angle-independent pitching moment at the aerodynamic center from the moving center of pressure; the low-speed quarter-chord position is an approximation, not a universal location.

Official NASA Glenn Research Center article. Sections Center of Pressure and Angle of Attack give the pressure-moment ratio and explain why its location changes with the pressure field. The Aerodynamic Force section distinguishes using that point from retaining a force and pitching moment about an aerodynamic center.

Originating manufacturer description of multicomponent force plates. The six-output measurement description specifies three force and three moment components used to calculate center of pressure. No particular sensor geometry, calibration coefficients or claimed accuracy values are adopted.

Official faculty profile. The heading and Biography identify Kris Hauser and describe robot planning/control, computational limits and uncertain dynamics. The page labels its image Kris Hauser and links ws.engr.illinois.edu/directory/viewphoto.aspx?photo=19910&s=300 .

Author-hosted draft textbook; title page identifies Kris Hauser and the University of Illinois at Urbana-Champaign. Consulted chapter: motion.cs.illinois.edu/RoboticSystems/AdvancedTopicsInPlanning.html . Chapter 12, Contact modeling and Equilibrium conditions, gives unilateral normal reactions, force/torque balance and the horizontal support-polygon model; Multi-modal motion planning, Example 1, notes the limits of the projected hull test on irregular terrain. The numerical reactions and plots in the linked support-polygon article are independent illustrative calculations.

Chapter 12, Manipulation planning and locomotion planning: contact selection and configuration-space motion must be reasoned about together because making or breaking contact changes the system’s dynamics and constraints.

Chapter 8, Stating the motion planning problem and Point-to-point path planning: a continuous configuration-space path must satisfy constraints along its entire length; the chapter distinguishes geometric path planning from dynamics and timing. Completeness and optimality and Explicit vs implicit plans separately discuss finite computation and execution policies.

Chapter 9, C-obstacles for rotational motion and Motion planning in SE(2): orientation-indexed configuration-space obstacle slices, periodic angular grid adjacency and the effect of robot radius on geometric motion bounds.

Primary institutional research account: news.mit.edu/2015/cheetah-robot-lands-running-jump-0529 . Jennifer Chu, MIT News Office, 29 May 2015. See, run, jump describes onboard LIDAR, obstacle estimates, stride adjustment and motor-force planning; later paragraphs distinguish treadmill from indoor-track trials and their available planning distance. The account concerns that 2015 demonstration, not every later MIT Cheetah version.

Primary IFR classification document: ifr.org/img/worldrobotics/Sources___Methods_WR_2025_Industrial_Robots.pdf . World Robotics 2025, Sources and methods, Section 1.7.1, printed p. 28, reproduces ISO 8373:2021 definitions of robot and robot categories. A robot combines a programmed actuated mechanism with some autonomy; the narrower industrial definition includes a multipurpose manipulator and at least three programmable axes. Used as a dated definition/classification source, not a claim about current market totals.

Primary instrument-manufacturer explanation of three- and four-point flexural tests. The page emphasizes specimen dimensions, support span and loading span in converting force and deflection to flexural quantities. Used for experimental configuration and reporting conventions; the explicit midpoint-deflection formula in the article is an independent Euler-Bernoulli calculation.

Primary MIT mechanics handout, Stresses Around a Circular Hole. One-page derivation summary uses an Airy stress function and displays circular-hole stress components, traction-free hole conditions, remote uniaxial tension and the factor-three maximum. It supplies the infinite-plate model, not finite-width or bending correction factors.

Primary MIT teaching document: ocw.mit.edu/courses/3-11-mechanics-of-materials-fall-1999/9cb0de418008f7516c08a7df6b91bb5c_MIT3_11F99_expt.pdf . David Roylance, 23 February 2001, as printed on the first page. Photoelasticity subsection, printed pp. 5–8: stress-dependent birefringence; p. 6 gives the stress-optical law and its wavelength-dependent coefficient; pp. 7–8 describe crossed-polarizer analysis and fringe interpretation. The OCW file listing calls the item Experimental Solutions; the document itself is headed Experimental Strain Analysis.

NACA-TN-740, 1 December 1939. Verified NTRS record and abstract: aluminum-alloy plate, two bending loads, strain/deflection measurements and distinct gross/net reference factors. Byline retained as C. Dumont.

The NTRS Authors metadata explicitly lists “Dumont, C (Aluminum Company of America)”; no expansion of C. is supplied. Its Abstract gives measured peak-stress ratios of 1.59 relative to the computed net-section stress and 1.85 relative to a solid plate of the same dimensions under the same bending forces. Locator: ntrs.nasa.gov/citations/19930081505 , Authors and Abstract.

Bending Test: adjustable four-point fixtures, 100-kN Instron 4400 frames, computerized load/deflection records and notched specimens.

MIT 2.002 laboratory module 4 (Spring 2004). §§4.1, 5.1, 6–7: circular-hole stresses, reference-area conventions and experimental apparatus.

Primary title page identifies Gregory F. Heath, Robert R. Filler and Jie Tan, The Boeing Company, May 2002. Introduction, printed pp. 1–2, describes the 250-horsepower proof-of-concept split-torque face-gear gearbox. Section VIII, printed pp. 71–78, documents torque calibration and split measurement; Conclusions, printed pp. 84–85, summarize the tested arrangement. The NTRS abstract reports nearly even load division using floating pinions.

Summary, printed p. iii (PDF p. 5), and Conclusions, printed p. 84 (PDF p. 91), report approximately 48%/52% input-pinion torque division and 57%/43% idler load sharing, with strain/load calibration limitations. Introduction, printed p. 1, identifies the cantilevered floating-pinion mount. The Conclusions describe an off-90-degree tapered transmission and the modified fixed-pinion comparison, which transmitted nearly all its load through the upper face-gear mesh.

Summary, printed p. iii: slow-roll testing used weights, pulleys and cables to apply torques, with tooth-root strain gauges. The full two-pinion/two-idler configuration gave input mesh division approximately 48%/52% and idler division approximately 57%/43%; the report explains the dependence on backlash setting and strain-based inference.

Calculation of load capacity of spur and helical gears — Part 1: Basic principles, introduction and general influence factors. Edition 2, September 2006, corrected March 2007. Section 7.3.1 discusses loaded contact assessment; §7.4.2, equation (38), printed p. 41, defines the contact face-load factor as maximum line-load intensity divided by mean intensity. This is the cited historical edition; the publisher records its replacement by the 2019 edition.

Primary title page gives David G. Lewicki, Paula J. Dempsey, Gregory F. Heath and Perumal Shanthakumaran, October 2009. Printed pp. 1–3 describe the 24 gear sets, test facility, vibration acquisition and oil-debris instrumentation; pp. 4–5 relate inspection observations to detection performance.

Gear Technology published version, November/December 2010, printed pp. 48–59. The article repeats the four original bylines. Author biographies on printed p. 59 document Paula J. Dempsey's NASA aerospace-research work, Gregory F. Heath's Boeing rotorcraft-drive role, and Perumal Shanthakumaran's Boeing condition-monitoring role as of that publication. Initial-only names are retained as printed.

Primary manufacturer catalogue, section B.2, “Arrangements and their bearing types”, printed p. 70: locating supports establish shaft axial position; non-locating supports accommodate relative axial displacement from thermal expansion and tolerance accumulation. The catalogue distinguishes locating/non-locating, adjusted and floating bearing arrangements.

Primary title page identifies David G. Lewicki and June 1986. The NTRS identifier starts with 1987 but the publication date is 1986. Summary, printed p. 1, and Summary of Results, printed p. 11, describe calculated dynamic tooth loads and predicted pitting-fatigue life for low-contact-ratio spur gears.

Summary and Introduction, printed p. 1 (PDF p. 3), specify the modified TELSGE tooth-stiffness model and stiffness–dynamic-load iteration; tooth stiffness and dynamic loads were calculated as functions of contact position and speed. These are model calculations, distinct from the 2009 endurance-monitoring experiment cited separately.

Manufacturer engineering reference, §4.0 “Bearing Loads”: case (a), radial shaft load between bearings; case (b), overhung radial load; case (f), external spur gears; case (g), parallel-shaft helical gears and axial thrust. The indexed primary page distinguishes these support arrangements.

Primary function documentation, Description and the orderlist input: follows requested rotation-related orders using signal samples, sampling frequency and shaft RPM data. The consulted documentation identifies release R2026b. Order selection is independent of whether a particular tracking implementation uses angular resampling.