# Trajectory Planning with Electronic CamsTrajectory Planning with Electronic Cams

DN Staff

November 16, 2010

What do Leonardo da Vinci and theNautilus exercise machine have in common? Leonardo da Vinci invented the camhammer (see photo) around 1497 and the Nautilus exercise machine, inventedaround 1970, uses a cam to modulate resistance. The cam - an irregularly shapedmember on a rotating shaft that transfers motion - has been around forcenturies. Up until recently, the study of cam design and application wasfoundational in a mechanical engineering curriculum. But today, it seems itsstudy is nowhere to be found.

In mechatronic design, integration isthe key as complexity has been transferred from the mechanical domain to theelectronic and computer software domains. Cams are a prime example of thatmechatronic principle as mechanical cams are gradually being replaced byelectronic cams. But transfer implies that we first understand the fundamentalprinciples in the mechanical domain. Since MEs aren't learning cam fundamentalsanymore and it was never part of an EE's training, motion systems today mostoften use crude motion trajectories that stress the machine and motor, produceunwanted vibrations, and result in poor performance.

To get up-to-date insight into thisissue, I met with Aderiano da Silva, an expert in motion control and automationmachine design for Rockwell Automation in Mequon, WI. His view is thattrajectory planning and its real-time implementation is not well understood andtherefore often neglected. It typically becomes an after-thought add-on - and acrude one at that.

Trajectory planning is the computationof motion profiles for the actuation system of automatic machines, e.g.,packaging machines, machine tools, assembly machines, industrial robots.Kinematic (direct and inverse) and dynamic models of the machine and itsactuation system are required. Desired motion is usually specified in theoperational space, while the motion is executed in the actuation space, andoften these are different. The trajectory is usually expressed as a parametricfunction of the time, which provides at each instant the corresponding desiredposition. Once the trajectory is defined, implementation issues include timediscretization, saturation of the actuation system and vibrations induced onthe load.

In past decades, mechanical cams havebeen widely used for transferring, coordinating and changing the type of motionfrom a master device to one or more slave systems. Replacing them areelectronic cams, with the goal to obtain more flexible machines, with improvedperformances, ease of re-programming and lower costs. With electronic cams, themotion is directly obtained by means of simpler mechanisms with electricactuators, properly programmed and controlled to generate the desired motionprofiles, which also allows synchronization of actuators on a position or timebasis.

Once the displacement and its durationhave been defined, the choice of the manner of motion from the initial to thefinal point has important implications with respect to the sizing of theactuators, the efforts generated on the structure and the tracking error. Theengineer must carefully consider the different types of point-to-pointtrajectories which could be employed with a specific system. Both time-domainand frequency-domain analyses must be performed on the complete system, i.e., actuator,mechanism and load, along with the motion profile, to achieve optimalperformance. Input shaping and feedforward control are two techniques used toimprove tracking performance.

A key reference is "Trajectory Planning for AutomaticMachines and Robots" by Luigi Biagiotti and Claudio Melchiorri. Knowledge fromthe past combined with new technologies results in innovation. Engineers mustnever forget this fact.

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