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This paper presents the analysis and design of a variable compression-ratio and displacement engine concept - the Alvar Cycle using a four-stroke engine-performance simulation. The Alvar-Cycle engine uses secondary pistons which reciprocate in auxiliary chambers housed in the cylinder head, at adjustable phase-angle differences from the primary pistons. The phase difference provides both the variable total engine displacement and compression ratio. Results indicate that the Alvar engine can operate at higher power density via a combination of higher intake boost and lower compression ratio to avoid knock at high loads, and capture the better thermal efficiency at higher compression ratios at part loads.