Epistemic agency is situated within social, cultural, and material contexts of learning. Making and inventing supports children's and families' creative thinking, problem-solving, and knowledge construction, through which they are positioned as active knowledge agents and their epistemic agency is represented. This article examines how the epistemic agency of children and parents shifted as they engaged in making activities in a museum-based makerspace. Through video-based, multimodal interaction analysis of thirteen cases, our findings demonstrate moment-by-moment transition patterns between child-led, parent-led, and equally-distributed epistemic agency. Our findings also show how these epistemic agency shifts emerged through the families' embodied interactions. By doing so, we reveal that (a) the lead epistemic agent role shifted over time during the inventing experience and (b) the epistemic agency of a parent and a child were relative to each other. This study contributes to the theoretical understanding of epistemic agency in situ during collaborative making activities as a fluid phenomenon as well as provides practical implications for museum-based makerspaces to support parent-child knowledge-building interactions during inventing.