Assembly configurations of planar multiloop mechanisms with kinematic limitations and spatial single-loop mechanisms

David Eric Foster, Purdue University

Abstract

This thesis examines the problem of enumerating and identifying the assembly configurations (ACs), or circuits, of planar and spatial mechanisms. An assembly configuration is a set of contiguous positions that a mechanism can assume without disassembly. The first topic addressed is planar multi-loop mechanisms, which are divided into two categories, single-input dyadic (SID) and non-single-input-dyadic (NSID). An SID mechanism is defined by adding one loop at a time such that there is one degree of freedom after each loop is added. All other planar mechanisms are NSID mechanisms. An automatic method is given to find the ACs of SID and NSID mechanisms with any number of loops, provided that the mechanism never has more than two degrees of freedom after each loop is added. Next, the same methods are applied to planar SID and NSID mechanisms with kinematic limitations, which are physical constraints that limit the motion of the mechanism, including joint limits, link interference, obstacle collision, and workspace constraints. Next, the simplest spatial mechanism namely the spherical mechanism is analyzed. The methods and results are very similar to those for the planar single-loop mechanism (SLM). These methods can be applied to spatial SLMs with revolute, cylindric, and prismatic joints, if there are at least three cylindric or prismatic joints. The final topic is general spatial SLMs with one degree of freedom. Eleven types of spatial SLMs are identified, and classified into four groups: mechanisms analyzed by removing two links, mechanisms analyzed by removing a link, mechanisms analyzed by disconnecting a 3-DOF joint, and mechanisms analyzed by changing a 1-DOF joint into a 2-DOF joint. A search is performed to find all positions of the relaxed mechanism (or chain) that meet the original constraints, leading to the identification of the ACs. The most common application is precision-point synthesis; in particular, ensuring that each design point lies on the same AC. Otherwise, the mechanism must be disassembled to move between positions, and is therefore useless. Another possible application is to investigate if a mechanism may inadvertently snap from one AC to another due to excessive dimensional tolerances in its link lengths.

Degree

Ph.D.

Advisors

Cipra, Purdue University.

Subject Area

Industrial engineering|Computer science

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