Cell intercalation, the dynamic exchange of cellular neighbors, is fundamental to embryonic morphogenesis, tissue homeostasis, and wound healing. Despite extensive study in complex tissues, the minimal mechanical requirements driving intercalation remain poorly understood due to confounding tissue level interactions. Here, we present a novel morphogenesis-on-chip assay utilizing micropatterned cell quadruplets. This system isolates the elementary unit of intercalation while enabling quantitative force and shape measurements. Cross-shaped micropatterns generate stable four cell configurations in MDCK epithelial cells. Surprisingly, these cells spontaneously undergo T1 transitions autonomously. We combined live imaging with force inference and traction force microscopy, which revealed that intercalation emerges from two distinct mechanisms: interfacial tension dynamics and differential cell migration. Specifically, we show a correlation between central junction shrinkage and increased relative tension. Similarly, we show a correlation between central junction shrinkage and migratory forces. We successfully adapted the assay to Xenopus mesoderm cells, revealing conserved mechanical principles across cell types. Furthermore, experimentally derived effective energy landscapes closely match theoretical vertex model predictions, and suggest a dominant role for migratory forces in driving intercalation. This confirms that our minimal system recapitulates the fundamental physics of intercalation. This approach provides the first quantitative framework for studying intercalation mechanics in isolation and establishes a versatile platform for investigating morphogenetic processes.