Final Report Finite Element Analysis of a Toggle Mechanism: Sensitivity to Link Sizes and Compliance Material By: Joseph Hughes MANE 6980

Toggle Mechanism Finite Element Analysis was Divided into Three Evaluations Analysis of a baseline mechanism was establish to provide a basis for the evaluation of any changes Sensitivity to Linkage Length Use varying length of linkages to model potential machining tolerances and their effect on the stresses within the linkage Sensitivity to Compliant Material Vary the stiffness of the compliant material element within the linkage to determine their impact on the stresses within the linkage

The Toggle Mechanism was Analyzed in ABAQUS The toggle linkage was modeled in ABAQUS with two links, a slide, and a stop. To simulate the motion of a toggle mechanism through the toggle point the center pin was displaced downward.

Mesh Concentrated in Areas of Suspected Mesh was concentrated in areas of suspected high stress Linear brick elements with incompatible modes utilized for low computational cost and due to use of bubble shape functions, have similar accuracy of higher order elements

Force Within Over-Toggle Mechanism Is Sensitive To Link Length The pins of the linkage were not explicitly modeled, but using the “hinge connector” built into the ABAQUS program one was able to still evaluate the forces in the pins A space was initially set between the slide and stop to allow some travel of the mechanism prior to contact 0.012” Initial Gap

Displacement of the Center Pin Causes Movement of Linkage The motion of the linkage is shown in the figure below Stress in the links within the linkage are reported along with the force within the center pin

Results of Evaluation of the Baseline Mechanism Do to use of connector, unrealistic stress concentration around pin holes, but provides realistic pin forces to evaluate stress in pin and links Force plots from the center pin were evaluated in vertical and horizontal directions (see figure below for location of forces) Vertical Horizontal

Forces within the Pin Illustrate Theory of Toggle Mechanism As the pin is displaced the vertical force increases due to slide contacting the stop, but decreases and goes to 0 lbf as the links align due to infinite mechanical advantage afforded by linkage The horizontal force in the pin increases to a maximum at the toggle point of the mechanism Vertical ForceHorizontal Force

Baseline Analysis Tested for Verification A mesh density study was performed Roughly tripling the number of elements resulted in approximately 1.5% decrease in the horizontal force in the pin and max stress 0.3% increase An analysis was performed with quadratic reduced integration elements Horizontal pin force was reduced by 1.8%, but max stress was increase by 3.8% Decreasing the time step by a factor of two had no effect on the force within the pin and a decrease of 0.05% in max stress

Small Increases in Link Length Creates Large Variations in Pin Force Table below provides results of evaluation Increase of only 0.002” to the links increases force by 78%.

Large Decreases in Stiffness of Compliant Material have Little Effect on Pin Force Table below provides results of evaluation Cutting the Elastic Modulus from the baseline by 4 resulted in a 10% decrease in pin force

Conclusion The pins is linkages like this are very highly loaded The increase in length of the links a small significantly increases the forces within the mechanism This is likely why most toggle mechanism (such as a pair of vise- grip pliers) come with an adjustment feature A significant reduction in stiffness (50-75%) of the compliant material reduced the forces within the links, but only by a small percentage The forces and stresses within the linkage are driven by compression and while the reduction in stiffness of the material reduces the amount that the links need to compress it is not as significant as the increase from the linkage length.

References Were Used Throughout The Analysis [1] Tso, Pei-Lum. “The Kinematic Synthesis of Toggle Clamps.” Journal of Manufacturing Science and Engineering, Vol. 120 August 1998, pages [2] Zhang, Yi. “Introduction to Mechanisms”, Chapter 4.0. Carnegie Mellon University accessed 7/26/12, [3] Matweb.com AISI Type 304 Stainless Steel, Accessed on 7/26/12, 27e&ckck=1 [4] Standard Specification for Stainless Steel Bars and Shapes, dated 1 May 2010, Specification Number ASTM-A276 [5] SAE J467b, October 68. Society of Automotive Engineers, Inc [6] Standard Specification for Precipitation-Hardening Stainless and Heat-Resisting Steel Plate, Sheet, and Strip, dated 1 March 2006, Specification Number ASTM-A693 [7] ABAQUS/CAE “Abaqus User Manual.” Dassault Systemes, Providence, RI, 2011