[1][2] The emphasis on geometry means that the links of the robot are modeled as rigid bodies and its joints are assumed to provide pure rotation or translation.
The relationship between mass and inertia properties, motion, and the associated forces and torques is studied as part of robot dynamics.
[3] The reverse process that computes the joint parameters that achieve a specified position of the end-effector is known as inverse kinematics.
For serial manipulators this requires solution of a set of polynomials obtained from the kinematics equations and yields multiple configurations for the chain.
For parallel manipulators, the specification of the end-effector location simplifies the kinematics equations, which yields formulas for the joint parameters.
The time derivative of the kinematics equations yields the Jacobian of the robot, which relates the joint rates to the linear and angular velocity of the end-effector.
The principle of virtual work yields a set of linear equations that relate the resultant force-torque six vector, called a wrench, that acts on the end-effector to the joint torques of the robot.