This　article　proposes　two　types　of　lockable　spherical　joints　which　can　perform　three　different　motion　patters　by　locking　or　unlocking　corresponding　rotational　axes.　Based　on　the　proposed　lockable　spherical　joints,　a　general　reconfigurable　limb　structure　with　two　passive　joints　is　designed　with　which　the　conceptual　designs　of　two　types　of　Exechon-like　parallel　kinematic　machines　are　completed.　To　evaluate　the　stiffness　of　the　proposed　Exechon-like　parallel　kinematic　machines,　an　expanded　kinetostatic　model　is　established　by　including　the　compliances　of　all　joints　and　limb　structures.　The　prediction　accuracy　of　the　expanded　stiffness　model　is　validated　by　numerical　simulations.　The　comparative　stiffness　analyses　prove　that　the　Exe-Variant　parallel　kinematic　machine　claims　competitive　rigidity　performance　to　the　Exechon　parallel　kinematic　machine.　The　present　work　can　provide　useful　information　for　further　investigations　on　structural　enhancement,　rigidity　improvement,　and　dynamic　analyses　of　other　Exechon-like　parallel　kinematic　machines.　©　2017,　©　The　Author(s)　2017.