Cutting insert, cutting tool, and method of manufacturing machined product

A cutting insert, comprising:

• a body member having a columnar shape, and comprising:
• an upper surface comprising at least one corner part;
• a lower surface opposed to the upper surface;
• a side surface between the upper surface and the lower surface, comprising:
• a front side surface;
• an outer side surface;
• an inner side surface opposed to the outer side surface;
• and
• a corner region located between the front side surface and the outer side surface;
• and
• a through hole penetrating through the center of the upper surface and the center of the lower surface;
• and
• a cutting member located at the corner region, and comprising:
• at least three surfaces;
• and
• a cutting edge at an intersecting portion of two of the at least three surfaces,
• the cutting edge comprises:
• a first cutting edge extending in a direction from the upper surface toward the lower surface;
• and
• a second cutting edge extending in a direction along the lower surface,
• wherein, in a plan view of the lower surface, a first distance between the through hole and the front side surface is greater than a second distance between the front side surface and a rear end of the cutting member,
• wherein the cutting member does not touch the upper surface,
• wherein a third distance between the second cutting edge and the upper surface is greater than a fourth distance between the upper surface and the lower surface,
• wherein the lower surface comprises a protruding part, and
• wherein the third distance is greater than a fifth distance between the upper surface and the protruding part.