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

A cutting insert, comprising:

• an upper surface having a polygonal shape, the upper surface comprising
• a first upper corner,
• a first upper side extended from the first upper corner, and
• a second upper side extended from the first upper corner;
• a lower surface having a polygonal shape, the lower surface comprising
• a first lower corner located below the first upper corner,
• a first lower side located below the second upper side and extended from the first lower corner, and
• a second lower side located below the first upper side and extended from the first lower corner;
• a lateral surface located between the upper surface and the lower surface;
• an upper cutting edge located on an intersection of the upper surface and the lateral surface;
• and
• a lower cutting edge located on an intersection of the lower surface and the lateral surface,
• wherein
• the lateral surface comprises
• a first lateral surface connecting to the first upper side and the second lower side,
• a second lateral surface connecting to the second upper side and the first lower side, and
• a third lateral surface located between the first lateral surface and the second lateral surface,
• an imaginary straight line passing through a center of the upper surface and a center of the lower surface is a central axis,
• the first lateral surface comprises a first concave part comprising
• a first constraining surface having a flat shape, and
• a first inclined surface closer to the first upper side than the first constraining surface, the first inclined surface extending away from a first virtual straight line as the first inclined surface extending towards the first upper side, the first virtual straight line passing through the first upper side and parallel to the central axis,
• the second lateral surface comprises a second concave part comprising a second constraining surface having a flat shape,
• the third lateral surface comprises a convex part having a convex shape in a cross section along the central axis,
• the first concave part and the second concave part are separated from each other by the convex part,
• the first constraining surface is located halfway between the upper surface and the lower surface in a direction along the central axis, and
• in a cross section orthogonal to the first upper side,
• a first point at the first constraining surface is located closer to the first virtual straight line than a second point at the first constraining surface, the first point at the first constraining surface being located between the first upper side and the second point at the first constraining surface in the direction along the central axis,
• an end point of the first constraining surface on a side of the lower surface is located on an outer side of the first virtual straight line, and
• a first point at the first inclined surface is located further away from the first virtual straight line than a second point at the first inclined surface, the first point at the first inclined surface being located between the first upper side and the second point at the first inclined surface in the direction along the central axis.