Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See Parameter IDs.
Parameter: Priority
ID_CA_JOINT_OBJECT_PRIORITYParameter: Bone
ID_CA_JOINT_OBJECT_BONE_ALIGNParameter: Axis
ID_CA_JOINT_OBJECT_BONE_AXISParameter: Align
ID_CA_JOINT_OBJECT_ALIGN_AXISParameter: Length
ID_CA_JOINT_OBJECT_LENGTHParameter: Display
ID_CA_JOINT_OBJECT_BONE_DISPLAYParameter: Size
ID_CA_JOINT_OBJECT_BONE_SIZE_MODEParameter: Size
ID_CA_JOINT_OBJECT_BONE_SIZEParameter: Display
ID_CA_JOINT_OBJECT_JOINT_DISPLAYParameter: Size
ID_CA_JOINT_OBJECT_JOINT_SIZE_MODEParameter: Size
ID_CA_JOINT_OBJECT_JOINT_SIZEParameter: Weight
ID_CA_JOINT_OBJECT_JOINT_IK_WEIGHTParameter: Stretch
ID_CA_JOINT_OBJECT_JOINT_IK_STRETCHParameter: Use Preferred
ID_CA_JOINT_OBJECT_JOINT_IK_PREFERRED_ROT_LINKParameter: Set
ID_CA_JOINT_OBJECT_JOINT_IK_PREFERRED_SETParameter: Weight
ID_CA_JOINT_OBJECT_JOINT_IK_PREFERRED_ROT_WEIGHTParameter: Preferred
ID_CA_JOINT_OBJECT_JOINT_IK_PREFERRED_ROTParameter: Strength
ID_CA_JOINT_OBJECT_JOINT_IK_LIMITROT_STRENGTHParameter: Limit Heading
ID_CA_JOINT_OBJECT_JOINT_IK_USE_ROT_HParameter: Limit Pitch
ID_CA_JOINT_OBJECT_JOINT_IK_USE_ROT_PParameter: Limit Bank
ID_CA_JOINT_OBJECT_JOINT_IK_USE_ROT_BParameter: Minimum Rotation
ID_CA_JOINT_OBJECT_JOINT_IK_MIN_ROTParameter: Maximum Rotation
ID_CA_JOINT_OBJECT_JOINT_IK_MAX_ROTParameter: Enable
ID_CA_JOINT_OBJECT_MIRROR_ENABLEParameter: Hub
ID_CA_JOINT_OBJECT_BONE_HUBParameter: Mirror
ID_CA_JOINT_OBJECT_JOINT_MIRROR_LINKParameter: Origin
ID_CA_JOINT_OBJECT_MIRROR_ORIGINParameter: Plane
ID_CA_JOINT_OBJECT_MIRROR_PLANEParameter: Object
ID_CA_JOINT_OBJECT_MIRROR_ORIGIN_LINKParameter: Mix
ID_CA_JOINT_OBJECT_MIRROR_COLOR_MIXParameter: Color
ID_CA_JOINT_OBJECT_MIRROR_COLOR